Pulley

Q. Three equal weights $A,B$ & $C$ each of mass $2\text{kg}$ are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in string connecting $B$ and $C$ approximately is

1. Zero
2. $3.3\text{N}$
3. $19.6\text{N}$
4. $13\text{N}$

Q.

Find the acceleration of the block A and B in the three situations shown in figure.

Q. State the third law of motion.

Q.

A body with a mass 5 kg is acted upon by a force $\overrightarrow{F}=\left(-3i+4j\right)$ $N$. If its initial velocity at t=0 is $\overrightarrow{v}=\left(6i-12j\right)m/s$, the time at which it will just have a velocity along the y-axis is

1. never

2. 10 s

3. 2 s

4. 15 s

Q. Two blocks A and B of same mass $m$ attached with a light string are suspended by a spring as shown in the figure. Find the acceleration of block A and B just after the string is cut.

1. $a_A=g(\uparrow ),a_B=g(\downarrow )$
2. $a_A=g(\downarrow ),a_B=g(\uparrow )$
3. $a_A=\frac{g}{2}(\uparrow )a_B=g(\downarrow )$
4. $a_A=\frac{3}{2}g(\uparrow ),a_B=\frac{3}{2}g(\downarrow )$

Q. Two blocks $m_1=5\text{gm}$ and $m_2=10\text{gm}$ are hung vertically over a light frictionless pulley as shown here. What is the acceleration of the masses when they are left free?

(where $g$ is acceleration due to gravity)

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

Q. The monkey $\text{B}$ shown in the figure is holding onto the tail of the monkey $\text{A}$ which is climbing up a rope. The masses of monkeys $\text{A}$ and $\text{B}$ are $5\text{kg}$ and $2\text{kg}$ respectively. If $\text{A}$ can tolerate a tension of $30\text{N}$ in its tail, what force should it apply on the rope in order to carry the monkey $\text{B}$ with it ? (take $g=10{\text{m/s}}^2$)

1. $T\ge 70\text{N}andT\le 85\text{N}$
2. $T\ge 60\text{N}andT\le 85\text{N}$
3. $T\ge 60\text{N}andT\le 105\text{N}$
4. $T\ge 70\text{N}andT\le 105\text{N}$

Q. A $50\text{kg}$ person stands on a $25\text{kg}$ platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upward at a steady rate if the force with which the person pulls the rope is

1. $500\text{N}$
2. $50\text{N}$
3. $250\text{N}$
4. $25\text{N}$

Q. Two pulley arrangements of figure given are identical. The mass of the rope in negligible. In fig(a), the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In fig(b), $m$ is lifted up by pulling the other end of the rope with a constant downward force $F=2mg$. The acceleration of $m$ in the two cases are respectively

1. $\frac{g}{3},g$
2. $\frac{g}{3},2g$
3. $g,\frac{g}{3}$
4. 3g, g

Q. Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force F applied on the upper string produces an acceleration of $2m/s^2$ in the upward direction in both the blocks. If T and T' be the tensions in the two parts of the string, then

1. T = 70.8 N and T'= 47.2 N
2. T = 58.8 N and T'= 47.2 N
3. T = 70.8 N and T'= 58.8 N
4. T = 70.8 N and T'= 0

Q. A spring having spring constant $k$ is cut into two parts in the ratio $1:3$. If these parts are connected in parallel then the equivalent spring constant for the combination will be:

1. $\frac{4k}{3}$
2. $k$
3. $\frac{16k}{3}$
4. $\frac{k}{4}$

Q.

A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is $(giveng=10m{s}^{-2})$

1. 

2. 

3. 

4. 

Q. Two blocks of masses $m_1$ and $m_2$ are connected as shown in the figure. The acceleration of the block $m_2$ is

1. $\frac{m_{2}g}{m_1+m_2}$
2. $\frac{m_{1}g}{m_1+m_2}$
3. $\frac{4m_{2}g-m_{1}g}{m_1+m_2}$
4. $\frac{m_{2}g}{m_1+4m_2}$

Q. Find the magnitude of acceleration (in ${\text{m/s}}^2$) of the system if all surfaces are smooth. $g=10{\text{m/s}}^2$.

1. 2
2. 3
3. 4
4. 6

Q. In the figure given below, with what acceleration does the block of mass $m$ will move?
(Pulley and strings are massless and frictionless)

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

Q. Two blocks A and B of equal masses $m\text{kg}$ are suspended with the help of ideal pulleys and string arrangement as shown in figure. Then acceleration $\left({\text{in m/s}}^2\right)$ of mass B will be:

1. $\frac{g}{3}{\text{m/s}}^2$
2. $\frac{5g}{3}{\text{m/s}}^2$
3. $\frac{4g}{3}{\text{m/s}}^2$
4. $\frac{2g}{5}{\text{m/s}}^2$

Q. If the mass of the body $A$ is $m$. Find the mass of the body $B$ in terms of mass of the body $A$ for the system to be in equilibrium.

1. $3m$
2. $2m$
3. $\frac{m}{2}$
4. $\frac{m}{3}$

Q. Three particles of masses $1\text{kg},2\text{kg}$ and $3\text{kg}$ are subjected to forces $(3\hat{i}-2\hat{j}+2\hat{k})\text{N}$, $(-\hat{i}+2\hat{j}-\hat{k})\text{N}$ and $(\hat{i}+\hat{j}+\hat{k})\text{N}$ respectively. The magnitude of the acceleration of the CM of the system is -

1. $\frac{\sqrt{11}}{6}{\text{m/s}}^2$
2. $\frac{\sqrt{14}}{6}{\text{m/s}}^2$
3. $\frac{11}{6}{\text{m/s}}^2$
4. $\frac{22}{6}{\text{m/s}}^2$

Q.

Why is it easier to fetch water from a well using a pulley?

1. Because rolling friction is lesser than sliding friction

2. Weight of bucket increases while pulling up

3. While pulling up you are pulling bucket's weight and your hand's against gravity while using pulley you are effectively pulling only the weight of the bucket - the weight of your hand.

4. While pulling up the bucket feels a pseudo acceleration in the downward direction which increases the total weight.

Q. Immediately on cutting the taut string, the acceleration of one of the blocks is found to be $2m{s}^{-2}.$ If $m_1=6kg,m_2$ is equal to $(g=10m{s}^{-2})$

1. $4kg$
2. $5kg$
3. $2kg$
4. $8kg$

Q. A block of mass $m$ is released from the top of a wedge of mass $M$ as shown in the figure. Find the displacement of the wedge on the horizontal ground, when the block reaches the bottom of the wedge.

Neglect friction everywhere.

1. $\frac{mh\tan \theta }{M+m}$
2. $\frac{mh\tan \theta }{M-m}$
3. $\frac{mh\cot \theta }{M+m}$
4. $\frac{mh\cot \theta }{M-m}$

Q. Three blocks $A,B$ and $C$ of equal weights of mass $2\text{kg}$ each are hanging on a string passing over a fixed pulley as shown in figure. What is the tension in the string connected between block $B$ and $C$?

1. $12\text{N}$
2. $13.33\text{N}$
3. $3.3\text{N}$
4. $19.6\text{N}$

Q.

A block of mass m is connected with another block of mass 2m by a light spring. 2m is connected with a hanging mass 3m by an inextensible light string. At the time of release of block 3m?

1. Tension in the string is $\frac{6}{5}mg.$

2. Acceleration of m is zero.

3. Acceleration of 3m is $\frac{g}{2}.$

4. Acceleration of 2m is $\frac{3g}{5}.$

Q. In the figure shown, find the force exerted by the pulley at the support. Make necessary assumptions and take $g=10m/s^2$

.

1. $72N$
2. $16N$
3. $32N$
4. $64N$

Q. Find the force exerted at the support $S$ in terms of ‘$m$’ if the system shown is in equilibrium.

1. $3\text{mg}$
2. $2\text{mg}$
3. $4\text{mg}$
4. $5\text{mg}$

Q. In the figure, all pulleys are massless and strings are light. Take $g=10m{s}^{-2}$
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) 1 kg block}& \text{(p) will remain stationary}\\ \text{(b) 2 kg block}& \text{(q) will move down}\\ \text{(c) 3 kg block}& \text{(r) will move up}\\ \text{(d) 4 kg block}& \text{(s)}5m/s^2\\ & \text{(t)}10m/s^2\end{array}$

1. $a-p;b-q;c-r;d-p$
2. $a-r,t;b-p;c-q;d-q,s$
3. $a-p;b-q;c-r,s;d-p$
4. $a-p,t;b-q;c-r;d-p,s$

Q. In the figure shown, the tension at the midpoint of the rope of mass $3\text{kg}$ (point $B$) is $13\text{N}$. Find the force pulling the $5\text{kg}$ body.

1. $10\text{N}$
2. $16\text{N}$
3. $20\text{N}$
4. $25\text{N}$

Q. Two unequal masses of $1kg$ and $2kg$ are connected by an inextensible light string passing over a smooth pulley as shown in the figure. A force $F=20N$ is applied on $1kg$ block. Find the acceleration of either block. $(g=10m/s^2)$ in $m/s^2$

Q. In the arrangement shown in figure, $m_A=m_B=2\text{kg}$. String is massless and pulley is frictionless. Block $B$ is resting on a smooth horizontal surface, while friction coefficient between block $A$ and $B$ is $0.4$. The maximum horizontal force $F$ that can be applied so that block $A$ does not slip over the block $B$ ($g=10\text{m}/s^2$) is

1. $25\text{N}$
2. $20\text{N}$
3. $40\text{N}$
4. $30\text{N}$

Q. A uniform rod of length $2.0\text{m}$, specific gravity $0.5$ and mass $2\text{kg}$ is hinged at one end to the bottom of a tank of water (specific gravity = $1.0$) filled upto a height of $1.0\text{m}$ as shown in the figure. Taking the case $\theta \ne 0^{\circ }$, the force exerted by the hinge on the rod is $(g=10{\text{m/s}}^2)$

1. $8.3\text{N}$ downwards
2. $10.2\text{N}$ upwards
3. $6.2\text{N}$ upwards
4. $4.2\text{N}$ downwards