Connected Bodies & Pulleys

Three blocks of different masses connected with inextensible string are pulled by a force $F$ on a frictionless surface as shown in the figure. The ratio of tensions $T_1$ to $T_2$ is

An inextensible string passing over a smooth pulley connects two blocks of masses $m_1$ and $m_2$ ($m_2 > m_1$) vertically. If the acceleration of the system is $\left(\frac{g}{n}\right)$, then the ratio of masses $\left(\frac{m_2}{m_1}\right)$ is

A block of mass M is lying on a horizontal frictionless surface. One end of the uniform rope of half the mass of the block is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. The tension in the middle of the rope will be

Three masses $m_1 = 4\text{ kg}, m_2 = 4\text{ kg}$ and $m_3 = 6\text{ kg}$ are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of $T_1/T_2$ is

______

(take $g = 10\text{ m/s}^{2}$)

A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^\circ$ with horizontal. A block $X$ with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge ( $Y$) is pulled toward right with constant force $(f)$ of 24 N. Taking the block $X$ at rest at $t = 0$, the time taken by it to slide down 8.8 m on the slope, while $Y$ is on the move, is ______ s.

$($ take $\tan(37^\circ) = 3/4$ and $g = 10\text{ m/s}^{2})$

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration $a_0$. The angle between the inclined plane and ground is $\theta$ and its base length is $L$. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is ________.

A box of mass $5\text{ kg}$ is pulled by a cord, up along a frictionless plane inclined at $30^\circ$ with the horizontal. The tension in the cord is $30\text{ N}$. The acceleration of the box is (Take $g = 10\text{ m s}^{-2}$)

Two blocks of masses 6 kg and 4 kg are placed in contact with each other on a smooth surface as shown. If a force of 5 N is applied on a heavier block, the force on the lighter block is

A horizontal force $10\text{ N}$ is applied to a block $A$ as shown in figure. The mass of blocks $A$ and $B$ are $2\text{ kg}$ and 3 $\text{kg}$ respectively. The blocks slide over a frictionless surface. The force exerted by block $A$ on block $B$ is:

Three blocks $A, B$ and $C$ are pulled on a horizontal smooth surface by a force of $80\text{ N}$ as shown in figure

The tensions T$1$ and T$2$ in the string are respectively:

Three blocks $M_1, M_2, M_3$ having masses $4\text{ kg}, 6\text{ kg}$ and $10\text{ kg}$ respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope $1, T_1$ when they are moving upward with acceleration of $2\text{ ms}^{-2}$ is __________ $\text{N}$ (if $g = 10\text{ m/s}^{2}$).

Two identical blocks each of mass ' M ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' $m$ ' is now placed on the block B. The acceleration with which the two blocks move together is [g = gravitational acceleration]

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$, then the ratio of the masses $\frac{m_2}{m_1}$ is:

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$, then the ratio of the masses $\frac{m_1}{m_2}$ is:

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g/8$, then the ratio of masses is:

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2\text{ kg}$ is:

As shown in figure, a $70\text{ kg}$ garden roller is pushed with a force of $\vec{F} = 200\text{ N}$ at an angle of $30^\circ$ with horizontal. The normal reaction on the roller is

(Given $g = 10\text{ m s}^{-2}$)

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s$2$)

Two bodies of masses $m_1 = 5\text{ kg}$ and $m_2 = 3\text{ kg}$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $m_1$ will be: [Take $g = 10\text{ ms}^{-2}]$

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = $\sqrt{x}$N as shown in figure.

The value of x = _____________.

In the diagram shown, the normal reaction force between 2 kg and 1 kg is (Consider the surface, to be smooth):

(Given g = 10 ms${}^{-2}$)

A block 'A' takes 2 s to slide down a frictionless incline of 30$^\circ$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45$^\circ$, the time taken by the block, to slide down the incline, will be approximately:

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' hanging on one side and rest of its length '$L - l$' is hanging on the other side of the pulley. At a certain point of time, when $l = \frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of x is __________.

A system of 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is __________ N when 6th ball just leaves the table.

Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_2$ is twice that of $M_1$, the acceleration of the system is $a_1$. When the mass $M_2$ is thrice that of $M_1$, the acceleration of the system is $a_2$. The ratio $\frac{a_1}{a_2}$ will be:

Three masses $M = 100\text{ kg},\ m_1 = 10\text{ kg}$ and $m_2 = 20\text{ kg}$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $F$ is applied on the system so that the mass $m_2$ moves upward with an acceleration of $2\text{ ms}^{-2}$. The value of $F$ is:

( Take $g = 10\text{ ms}^{-2}$)

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{x}{5}$ Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)

In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement?

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be:

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s2)

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given m = 8 kg, M = 16 kg. Assume all the surfaces shown in the figure to be frictionless.

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is:

A block of mass $M$ is pulled along a smooth horizontal surface with a rope of mass $m$ by force $F$. The acceleration of the block will be

A block of mass m is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given an acceleration ‘a’ towards the right. The relation between a and $\theta$ for the block to remain stationary on the wedge is

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively

Three blocks A, B and C, of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is

Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upwards at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)

Two blocks of mass $M_1 = 20$ kg and $M_2 = 12$ kg are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is:

Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If M = 2m, then the stress produced in the wire is:

Two fixed frictionless inclined planes making an angle $30^\circ$ and $60^\circ$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

A block of mass $m$ is connected to another block of mass $M$ by a spring (massless) of spring constant $k.$ The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force on the block of mass $m.$

A block is kept on a frictionless inclined surface with angle of inclination $\text{'}\alpha\text{'}.$ The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to

Two masses $m_1 = 5\text{ kg}$ and $m_2 = 4.8\text{ kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? $\left(g = 9.8\text{ m/s}^{2}\right)$

A block of mass m is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block will be (g is acceleration due to gravity)

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m.$ If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block is

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M\text{ kg}$ hangs from the former one. Then the true statement about the scale reading is

Three identical blocks of masses $m = 2\text{ kg}$ are drawn by a force $F = 10.2\text{ N}$ with an acceleration of $0.6\text{ ms}^{-2}$ on a frictionless surface, then what is the tension (in $\text{N}$) in the string between the blocks $B$ and $C$?

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is

250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m then the load is lifted to 3 m. the efficiency of pulley system will be

Two masses as shown in the figure are suspended from a massless pulley. The acceleration of the system when masses are left free is

A mass of $1\text{ kg}$ is suspended by a thread. It is

(i) lifted up with an acceleration $4.9\text{ m/s}^{2}$,

(ii) lowered with an acceleration $4.9\text{ m/s}^{2}$.

The ratio of the tensions is