Rolling Motion

A solid sphere rolls without slipping on an inclied plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is

A solid sphere of mass $1$ kg rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}$ J. The speed of the center of mass of the sphere in cm s$^{-1}$ is

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane $\sqrt{\frac{x}{5}}$ where the value of $x$ is

A solid sphere rolls down from the top of an inclined plane. On reaching the bottom of the plane, its velocity is '$V_1$'. When the same sphere slides down from the top of the same plane of same height, its velocity on reaching the bottom is '$V_2$'. The ratio $V_1 : V_2$ is (neglect friction)

A solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder $(a_c)$ to that of the sphere $(a_s)$ is

A body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity 'V'. If the same body is a ring which rolls down the same inclined plane then linear velocity at the bottom of the plane is

An object of uniform density rolls up the curved path with the initial velocity $v_0$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_0^{2}}{10g}$ ( $g =$ acceleration due to gravity), the object is a ______.

A solid sphere $(A)$ of mass $5m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they start rolling without slipping with an acceleration of $a_A$ and $a_B$, respectively. The ratio of $a_A$ and $a_B$ is ______.

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t = 0$ the cylinder has a translational velocity $v_0 = 49\text{ m/s}$, perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is ______ seconds. (coefficient of kinetic friction $\mu_K = 0.25$ and $g = 9.8\text{ m/s}^{2}$)

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is:

A solid sphere at rests rolls down an inclined plane of vertical height $h$ without sliding. Its speed on reaching the bottom of plane is ( $g =$ acceleration due to gravity)

A disc of mass ' $m$ ' and radius ' $r$ ' rolls down an inclined plane of height ' $h$ '. When it reaches the bottom of the plane, its rotational kinetic energy is ( $g =$ acceleration due to gravity)

An inclined plane makes an angle $30^\circ$ with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ( $g =$ acceleration due gravity) ( $\sin 30^\circ = 0.5$)

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8\text{ m/s}$. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be:

A body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity V. If the same body is a ring which rolls down the same inclined plane then linear velocity at the bottom of plane is

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length ' $L$ ' and makes an angle $30^\circ$ with the horizontal. The speed of the particle at the bottom of the plane is $v_1$. If the angle of inclination is increased to $45^\circ$ while keeping $L$ constant. Then the new speed of the sphere at the bottom of the plane is $v_2$. The ratio $v_1^{2} : v_2^{2}$ is

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{x}{5}}$ where $x =$ ________.

A solid sphere rolling without friction on a horizontal surface with a constant speed of $2\text{ m/s}$, rolls up on an inclined ramp which is inclined at $30^\circ$. The maximum distance travelled by the sphere on the inclined ramp is (acceleration due to gravity $g = 10\text{ m/s}^{2}, \sin 30^\circ = \frac{1}{2}$)

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination $45^\circ$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $v$ in the direction shown, which one of the following options is correct ($P$ and $Q$ are any highest and lowest points on the wheel, respectively)?

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is _________.

An inclined plane makes an angle $30^\circ$ with horizontal. A solid sphere rolls down from the top of the inclined plane from rest without slipping has a linear acceleration along the plane equal to (where $g$ is acceleration due to gravity) (given $\sin 30^\circ = 0.5$)

A solid cylinder of mass ' $M$ ' and radius ' $R$ ' rolls down an inclined plane of height ' $h$ '. When it reaches the foot of the plane, its rotational kinetic energy is ( $g =$ acceleration due to gravity)

An inclined plane makes an angle of $30^\circ$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration ( $g =$ acceleration due to gravity, $\sin 30^\circ = 0.5$)

A cylinder is rolling down on an inclined plane of inclination $60^\circ$. Its acceleration during rolling down will be $\frac{x}{\sqrt{3}}\text{ m/s}^{2}$, where $x =$ ________ (use $g = 10\text{ m/s}^{2}$ ).

A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 6 J then total kinetic energy of the disc is

A body of mass $m$ slides down an incline and reaches the bottom with a velocity V. If the same mass were in the form of a disc which rolls down this incline, the velocity of the disc at bottom would have been

A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, it takes $t\text{ s}$. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1/2} t\text{ s}$, where $\alpha$ is _________.

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\frac{7}{x}$, where $x$ is _________.

A disc of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is:

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reach upto maximum heights $h_1$ and $h_2$ respectively, above the initial level. The ratio $h_1 : h_2$ is $\frac{n}{10}$. The value of $n$ is __________.

A solid circular disc of mass $50\text{ kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4\text{ m/s}$. The absolute value of work done on the disc to stop it is ________ J.

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is

A solid sphere rolls without slipping on an inclined plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is ___________.

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be _______ ms$^{-1}$.

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radii of gyration respectively $(k$sph $: k$cyl $)$ is $2 : \sqrt{x}$. The value of $x$ is ____________.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi : 22$ then, the value of its angular speed will be ____________ $\text{rad/s}$.

A solid sphere of mass $1\text{ kg}$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}\text{ J}$. The speed of the centre of mass of the sphere is __________ $\text{cm s}^{-1}$

A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder '$a_c$' to that of sphere '$a_s$' is

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^\circ$ and length $60\text{ cm}$. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is __________ $\text{ms}^{-1}$. (Given $g = 10\text{ ms}^{-2}$)

A solid cylinder of mass $3\text{ kg}$ is rolling on a horizontal surface with velocity $4\text{ m/s}$. It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spring is $200\text{ N/m}$. The maximum compression produced in the spring will be (assume collision between cylinder & spring be elastic)

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\text{ m/s}$ (as shown in figure). Maximum height with respect to the initial position covered by it will be __________ cm. (Take $g = 10\text{ m/s}^{2}$)

A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t = 0$, the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

A uniform disc of mass $0.5\text{ kg}$ and radius $r$ is projected with velocity $18\text{ m/s}$ at $t = 0$ s on a rough horizontal surface. It starts off with a purely sliding motion at $t = 0\text{ s}$. After $2\text{ s}$ it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after $2\text{ s}$ will be __________ $\text{J}$ (given, coefficient of friction is $0.3$ and $g = 10\text{ m/s}^{2}$ ).

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

A solid cylinder and a solid sphere, having same mass $M$ and radius $R$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be:

A solid cylinder is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $4\text{ ms}^{-1}$, is ____________ cm. (take g = $10\text{ ms}^{-2}$)

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be $\frac{1}{2}\sqrt{xgh}$ m/s. The value of x is ___________.

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is:

A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $\theta$ with the horizontal. The acceleration of the disc will be $\frac{2}{b}$ g sin$\theta$ where b is ____________. (Round off to the Nearest Integer) (g = acceleration due to gravity, $\theta$ = angle as shown in figure)

The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed $\sqrt{x}\,v_0$. Then the value of x is _____________.

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.

The correct statement for this situation is

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{\sqrt{x}}{2}$. Then, the value of x is _____________.

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't1'. When it rolls down the plane, it takes time t2. The value of $\frac{t_2}{t_1}$ is $\sqrt{\frac{3}{x}}$. The value of x will be _______________.

The following bodies,

(1) a ring

(2) a disc

(3) a solid cylinder

(4) a solid sphere,

of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ___________. [Mark the body as per their respective numbering given in the question]

A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30${}^\circ$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

[The coefficient of static friction, $\mu$s is 0.4]

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is:

A solid cylinder of radius $r$ and mass $M$ rolls down an inclined plane of height $h$. When it reaches the bottom of the plane, then its rotational kinetic energy is ($g =$ acceleration due to gravity)

A body slides down a smooth inclined plane having angle $\theta$ and reaches the bottom with velocity $v$. If a body is a sphere, then its linear velocity at the bottom of the plane is

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

A solid sphere rolls down from top of inclined plane, 7 m high, without slipping. Its linear speed at the foot of plane is $\left(g = 10\text{ m/s}^{2}\right)$

A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination $30^\circ$. The centre of mass of the cylinder has speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be, [take $g = 10\text{ m/s}^{2}$]

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane.: (i) a ring of radius R, (ii) a solid cylinder of radius R/2 and (iii) a solid sphere of radius R/4. If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph and hcyl on the incline. The ratio hsph/hcyl is given by :-

A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be: (Take g = 10 m/s2)

A string is wound around a hollow cylinder of mass 5 kg and radius 0.5m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string):

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt: (Kt + Kr) for the sphere is

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is:

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is

A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $\frac{\sin\theta_c}{\sin\theta_s}$ is:

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is Ffriction at point P? It is assumed that the cylinder does not slip.

A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of $\frac{3v^{2}}{4g}$ with respect to the initial position. The object is

A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A, the ball becomes air borne leaving at an angle of 30° with the horizontal. The ball strikes the ground at B. What is the value of the distance AB? (Moment of inertia of a spherical shell of mass m and radius R about its diameter = $\frac{2}{3}mR^{2}$)

A hoop of radius $r$ and mass $m$ rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it ceases to slip?

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

A round uniform body of radius $R,$ mass $M$ and moment of inertia $I$ rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $\theta$. The frictional force

An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_1}{F_2}$ is

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom?

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. then the fraction of total energy associated with its rotational energy will be

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (if radius of wheel is 1 m)

A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct?

A solid spherical ball rolls on a table. Ratio of its rotational kinetic energy to total kinetic energy is

A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on the inclined plane, then

The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height $h$ form rest without sliding is

If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by

A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom?

A solid homogenous sphere of mass $M$ and radius is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere