Pulley Problem

Q.

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

Q.

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 will be

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Q. Two blocks of mass $10\text{kg}$ and $2\text{kg}$ respectively are connected by an ideal string passing over a fixed smooth pulley as shown in figure. A monkey of mass $8\text{kg}$ starts climbing the string with a constant acceleration of $2{\text{ms}}^{-2}$ with respect to the string at $t=0$. Initially, the monkey is $2.4\text{m}$ from the pulley. Find the time taken by the monkey to reach the pulley.

1. $8\text{sec}$
2. $6\text{sec}$
3. $4\text{sec}$
4. $2\text{sec}$

Q.

A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude ? (c) What can be the maximum amplitude with which the two blocks may oscillate together ?

Q.

Two masses $8\mathrm{kg}$ and $12\mathrm{kg}$ are connected at the two ends of a string that goes over a frictionless pulley. Calculate the acceleration of the masses and the tension in the string. (take, $g=10m/s^2$)

1. $8m/s^2,144N$

2. $4m/s^2,112N$

3. $6m/s^2,128N$

4. $2m/s^2,96N$

Q.

A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig.5.19. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding?

Q.

A solid cylinder of mass m and radius R rests on a plank of mass 2m lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force F, find the acceleration of the cylinder and that of the plank.

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Q. In the following figure, a body of mass 'm' is tied at one end of a light string and this string is wrapped around the solid cylinder of mass 'M' and radius 'R'. At the moment, t = 0 the system starts moving. If the friction is negligible, angular velocity at time, t would be

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Q. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

1. g
2. 2g/3
3. g/3
4. 3g/2

Q. A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

1. $\frac{5g}{6}$
2. $\frac{2g}{3}$
3. $\frac{g}{2}$
4. g

Q. A spool is pulled at an angle $\theta$ with the horizontal on a rough horizontal surface as shown in the figure. If the spool remains at rest, the angle $\theta$ is equal to

1. ${\cos }^{-1}\left(\frac{R}{r}\right)$
2. $\pi -{\sin }^{-1}\left(\sqrt{1-\frac{r^2}{R^2}}\right)$
3. ${\sin }^{-1}\left(\frac{r}{R}\right)$
4. ${\cos }^{-1}\left(\frac{r}{R}\right)$

Q. A spherical body of radius 'R' rolls on a horizontal surface with linear velocity 'v'. Let $L_1$ and $L_2$ be the magnitudes of angular momenta of the body about centre of mass and point of contact P. Then,

1. $L_2=2L_1$ ; if radius of gyration K = R
2. $L_2=2L_1$ ; for all cases
3. $L_2>2L_1$ ; if radius of gyration K < R
4. $L_2>2L_1$ ; if radius of gyration K > R

Q.

In the given setup find the tension in the left and the right string? Assume string and pulley to be massless, surface and pulleys are frictionless.

1. None of these

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3. ;

4. ;

Q. A circular pulley of mass ${}^{\prime }{M}^{\prime }$ and radius ${}^{\prime }{R}^{\prime }$, is hinged at the centre. A long string is wound over this disc and two bodies of mass $m_1$ and $m_2$ are attached at it's free ends. Now the bodies are released. Find the accceleration of each body.

1. $\frac{(m_1-m_2)g}{M+(m_1+m_2)}$
2. $\frac{2(m_1-m_2)g}{M+(m_1+m_2)}$
3. $\frac{(m_1-m_2)g}{M+2(m_1+m_2)}$
4. $\frac{2(m_1-m_2)g}{M+2(m_1+m_2)}$

Q. Two masses of $6Kg$ and $4Kg$ are connected to the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released. Take $g=10{ms}^{-2}$.

Q. A small particle of mass $0.36\text{g}$ rests on horizontal turntable at a distance $25\text{cm}$ from the axis of spindle. The turntable is accelarated at a rate of $\alpha =\frac{1}{3}{\text{rad/s}}^2$. The frictional force that the table exerts on the particle $2\text{s}$ after the startup is

1. $40\mu N$
2. $60\mu N$
3. $30\mu N$
4. $50\mu N$

Q.

A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.

1. $\frac{3F}{7m},\frac{2F}{7m}$

2. $\frac{2F}{7m},\frac{3F}{7m}$

3. $\frac{4F}{7m},\frac{3F}{7m}$

4. $\frac{3F}{7m},\frac{4F}{7m}$

Q. An open cubical tank completely filled with water is kept on a horizontal surface. Its acceleration is then slowly increased to $2m/s^2$ as shown in the fig. The side of the tank is $1m$. The mass of water that would spill out of the tank in kg is 20×X , then the value of x is

Q. Two blocks of masses $M_1$ and $M_2$ are connected to each other through a light spring as shown in figure. If we push mass $M_1$ with force F and cause acceleration $a_1$ in right direction for mass $M_1$, what will be the magnitude of acceleration of $M_2$ ?

1. $F/M_2$
2. $F(M_1+M_2)$
3. $a_1$
4. $(F-M_1{a}_1)/M_2$

Q. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

1. 3g/2
2. g
3. 2g/3
4. g/3

Q.

A uniform chain of mass M and length L is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length x has reached the floor.

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Q. The initial speed of a bullet fired a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How fwr above the centre of the target the rifle be aimed in order to hit the target?

1. 1.0 m
2. 4.2 m
3. 6.1 m
4. 9.8 m

Q.

A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.

1. $\frac{3F}{7m},\frac{2F}{7m}$

2. $\frac{2F}{7m},\frac{3F}{7m}$

3. $\frac{4F}{7m},\frac{3F}{7m}$

4. $\frac{3F}{7m},\frac{4F}{7m}$

Q. Block A of mass $m/2$ is connected to one end of light rope which passes over a pulley as shown in the figure. Man of mass $m$ climbs the other end of rope with a relative acceleration of $g/6$ with respect to rope. Find acceleration of block A and tension in the rope.

1. $\frac{4g}{9},\frac{18mg}{13}$
2. $\frac{4g}{9},\frac{13mg}{18}$
3. $\frac{9g}{4},\frac{13mg}{18}$
4. $\frac{9g}{4},\frac{18mg}{13}$

Q. Find the mass of the block that a $40hp$ engine can pull along a level road at $15m{s}^{-1}$ if the coefficient of friction between block and road is $0.015$.

1. 2532 kg
2. 1353 kg
3. 3553 kg
4. 4553 kg

Q. In the following figure, a body of mass 'm' is tied at one end of a light string and this string is wrapped around the solid cylinder of mass 'M' and radius 'R'. At the moment, t = 0 the system starts moving. If the friction is negligible, angular velocity at time, t would be

1. $\frac{mgRt}{(M+m)}$
2. $\frac{2Mgt}{R(M+2m)}$
3. $\frac{2mgt}{R(M-2m)}$
4. $\frac{2mgt}{R(M+2m)}$

Q. A rope of negligible mass is wound around a hollow cylinder of mass 3 kg and radius 40 cm , what is the angular acceleration of the of the cylinder , if rope is pulled with a force of 30N ? What is the linear acceleration of the rope ? Assume there is no slipping .

Q. The uniform rod of mass $20kg$ and length $1.6m$ is pivoted at its end and swings freely in the vertical plane. Angular acceleration of rod just after the rod is released from rest in the horizontal position as shown in the figure is:

1. $\frac{15g}{16}$
2. $\frac{17g}{16}$
3. $\frac{16g}{15}$
4. $\frac{g}{15}$

Q. While launching a rocket of mass $2\times {10}^4$ kg, the $5\times {10}^{5}N$ is applied for $20s$. Calculate the velocity attained by the rocket at the end of $20s$

1. $300m{s}^{-1}$
2. $320m{s}^{-1}$
3. $100m{s}^{-1}$
4. $500m{s}^{-1}$

Q. 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 will be

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