Inertia, First & Second Laws

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it, are respectively:

At $t = 0$, a body of mass 100 g starts moving under the influence of a force $(5\hat{i} + 10\hat{j})\text{ N}$ After 2 s its position is $(2x\hat{i} + 5y\hat{j})\text{ m}$. The ratio $x : y$ is ______.

A 4 kg mass moves under the influence of a force $\vec{F} = \left(4t^3\hat{i} - 3t\hat{j}\right)\text{ N}$ where $t$ is the time in second. If mass starts from origin at $t = 0$, the velocity and position after $t = 2\text{ s}$ will be:

A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F = -kv$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$?

A constant force acts on two different masses independently and produces accelerations $A_1$ and $A_2$. When the same force acts on their combined mass, the acceleration produced is

A massless spring gets elongated by amount $x_1$ under a tension of 5 N. Its elongation is $x_2$ under the tension of 7 N. For the elongation of $(5x_1 - 2x_2)$, the tension in the spring will be,

An object with mass 500 g moves along x-axis with speed $v = 4\sqrt{x}$ m/s. The force acting on the object is:

A body of mass 2 kg moving with velocity of $\vec{v}_{in} = 3\hat{i} + 4\hat{j}$ ms$^{-1}$ enters into a constant force field of 6N directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ seconds, then velocity of the body when it emerges from force field is.

A block of mass 1 kg, moving along $x$ with speed $v_i = 10\text{ m/s}$ enters a rough region ranging from $x = 0.1\text{ m}$ to $x = 1.9\text{ m}$. The retarding force acting on the block in this range is $F_r = -kx\text{ N}$, with k $= 10\text{ N/m}$. Then the final speed of the block as it crosses rough region is.

Which one of the following is 'NOT' a contact force?

A body of mass $4\text{ kg}$ experiences two forces $\vec{F}_1 = 5\hat{i} + 8\hat{j} + 7\hat{k}$ and $\vec{F}_2 = 3\hat{i} - 4\hat{j} - 3\hat{k}$. The acceleration acting on the body is:

A particle moves in $x\text{-}y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{p}(t) = \hat{i}\cos(kt) - \hat{j}\sin(kt)$. If $k$ is constant, the angle between $\vec{F}$ and$\vec{p}$ will be:

The position vector of a particle related to time $t$ is given by

$\vec{r} = \left(10t\hat{i} + 15t^2\hat{j} + 7\hat{k}\right)\text{ m}$

The direction of net force experienced by the particle is:

A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels $24\text{ cm}$ through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

A body of mass $500\text{ g}$ moves along $x$-axis such that its velocity varies with displacement $x$ according to the relation $v = 10\sqrt{x}\text{ m/s}$ the force acting on the body is:-

At any instant the velocity of a particle of mass $500\text{ g}$ is $\left(2t\hat{i} + 3t^2\hat{j}\right)\text{ m s}^{-1}$. If the force acting on the particle at $t = 1\text{ s}$ is $(\hat{i} + x\hat{j})\text{ N}$. Then the value of $x$ will be:

A force on an object of mass 100 g is $\left(10\hat{i} + 5\hat{j}\right)$ N. The position of that object at t = 2 s is $\left(a\hat{i} + b\hat{j}\right)$ m after starting from rest. The value of $\frac{a}{b}$ will be ___________.

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to: [Use g = 10 ms${}^{-2}$].

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is 'x' N. The value of 'x' to the nearest integer is __________.

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile.

The correct applied force vs distance graph will be:

A force $\vec{F} = (40\hat{i} + 10\hat{j})\text{ N}$ acts on a body of mass 5 kg. If the body starts from rest, its position vector$\vec{r}$at time t = 10 s, will be:

A body of mass 2 kg moves under a force of $\left(2\hat{i} + 3\hat{j} + 5\hat{k}\right)$ N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is _____________. (Round off to the Nearest Integer)

A boy pushes a box of mass 2 kg with a force $\vec{F} = \left(20\hat{i} + 10\hat{j}\right)\text{ N}$ on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.

A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = $-\alpha$x2. The distance at which the particle stops:

A body of mass $2\text{ kg}$ is acted upon by two forces each of magnitude $1\text{ N}$ and inclined at $60^\circ$ with each other. The acceleration of the body in $\text{m/s}$ is [$\cos 60^\circ = 0.5$]

A particle moving in the xy plane experiences a velocity dependent force

$\vec{F} = k\left(v_y\hat{i} + v_x\hat{j}\right)$, where vx and vy are the

x and y components of its velocity$\vec{v}$. If$\vec{a}$is the

acceleration of the particle, then

which of the following statements is true for the particle?

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv2 where v is its speed. The maximum height attained by the ball is:

An aircraft is moving with uniform velocity $150\text{ m/s}$ in the space. If all the forces acting on it are balanced, then it will

A bullet of mass 20 g has an initial speed of 1 ms–1, just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10–2 N, the speed of the bullet after emerging from the other side of the wall is close to:

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constant, k1 and k2 will be:

A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to m$\gamma$u2 (where m is mass of the ball, u is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is:

A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is $\frac{1}{8}mv_0^2$, the value of k will be:

A particle of mass m is acted upon by a force F given by the empirical law F = $\frac{R}{t^2}v(t)$ If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot:

A Body of mass 5 kg under the action of constant force $\vec{F}$= Fx $\hat{i}$ + Fy $\hat{j}$ has velocity at t = 0 s as $\vec{v}$= (6$\hat{i} -$ 2$\hat{j}$) m/s and at t = 10 s as $\vec{v}$= + 6$\hat{j}$ m/s. The force $\vec{F}$is:

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

A particle of mass $m$ is at rest at the origin at time $t = 0$ It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

A body, under the action of a force $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k},$ acquires an accelerations of 1 m/s2. The mass of this body must be

A particle of mass 0.3 kg subjected to a force $F = -kx$ with $k = 15\text{ N/m}$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

An object of mass 3 kg is at rest. Now a force of $\vec{F}$= 6t2 $\hat{i}$ + 4t $\hat{j}$ is applied on the object then velocity of object at t = 3 sec. is

A force of $6\text{ N}$ acts on a body at rest and of mass $1\text{ kg}$. During this time, the body attains a velocity of $30\text{ m/s}$. The time for which the force acts on the body is

A $10\text{ N}$ force is applied on a body produce in it an acceleration of $1\text{ m/s}^2$. The mass of the body is

A force vector applied on a mass is represented as $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k}$ and accelerates with $1\text{ m/s}^2$. What will be the mass of the body?

Physical independence of force is a consequence of