Pulley

Q. The acceleration of block B in the figure will be

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

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 tension $T_1$ in the string. All surfaces are smooth.

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

Q. Find the tension $T_1$ in the string. Assume all surfaces to be smooth.

1. $3N$
2. $6N$
3. $2N$
4. $4N$

Q. In the arrangement shown, the acceleration of mass $2m$ is

1. $\frac{2}{3}$$g$
2. $\frac{2}{5}$$g$
3. $\frac{2}{8}$$g$
4. $\frac{1}{3}$$g$

Q.

What is tensional force?

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. 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 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. In the given diagram, with what force must the man pull the rope to hold the plank in position? $($Mass of the man is $80k$; neglect the weight of the plank, rope and pulley; take $g=10{m/s}^2)$

1. $200N$
2. $300N$
3. $600N$
4. $150N$

Q. If pulley shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4\text{kg}$ and $8\text{kg}$ respectively, then

1. $a_1=a_2$
2. $a_1=2a_2$
3. $2a_1=a_2$
4. $a_1=4a_2$

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

Q. Find the tension in the string between the pulleys and the acceleration of the blocks as shown in the figure. Assume that there is no slipping between the string and the pulleys.
[Given, mass of bigger pulley $=2m$, radius of bigger pulley $=R$, mass of smaller pulley $=m$ and radius of smaller pulley $=\frac{R}{2}$]

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

Q. In the figure shown, find the force exerted by the pulley at the support. Take $g=10{\text{m/s}}^2$ and assume that all surfaces are smooth.

1. $21\text{N}$
2. $42\text{N}$
3. $21\sqrt{2}\text{N}$
4. $\frac{21}{\sqrt{2}}\text{N}$

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 constant force F = $m_{2}g/2$ is applied on the block of mass $m_1$ as shown in figure. The string and the pulley are light and the surface of the table is smooth. The acceleration of $m_1$ is

1. $\frac{m_{2}g}{2(m_1+m_2)}$ towards left

2. $\frac{m_{2}g}{2(m_1+m_2)}$ towards right

3. $\frac{m_{2}g}{2(m_2-m_1)}$ towards right

4. $\frac{m_{2}g}{2(m_2-m_1)}$ towards left

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 $0.5$. 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. $30\text{N}$
4. $40\text{N}$

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

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. Force $F$ is applied on upper pulley. If $F=30t$ where $t$ is time in seconds. Find the time when $m_1$ loses contact with floor

Q. The masses of $4\text{kg}$ and $5\text{kg}$ are connected by a string passing over a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of $5\text{kg}$ mass is

1. $49{\text{m/s}}^2$
2. $5.44{\text{m/s}}^2$
3. $19.5{\text{m/s}}^2$
4. $2.72{\text{m/s}}^2$

Q. For the figure, both the pulleys are massless and frictionless. The right side pully can move. A force F, of any possible magnitude, is applied in horizontal direction. There is no friction between M and ground.
${\mu }_{1}and{\mu }_2$ are the coefficients of friction between the blocks as shown. Column I gives the different relations between ${\mu }_{1}and{\mu }_2$, and Column II is regarding the motion of M. Match the columns


$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{i.}& \text{If}\mu 1=\mu 2=0& \text{a.}& \text{May accelerate towards right}\\ \text{ii.}& \text{If}\mu 1=\mu 2\ne 0& \text{b.}& \text{May accelerate towards left}\\ \text{iii.}& \text{If}\mu 1>\mu 2& \text{c.}& \text{Does not accelerate}\\ \text{iv.}& \text{If}\mu 1<\mu 2& \text{d.}& \text{May or may not accelerate}\end{array}$

1. i - c; ii - c; iii - b, d; iv - a
2. i - c; ii - c; iii - b, d; iv - a, d
3. i - c; ii - c; iii - b; iv - a, d
4. i - c; ii - d, iii - b, d; iv - a, d

Q. As shown in figure, a man of mass $M$ is standing on a platform and holding an inextensible massless string which passes over a system of ideal pulleys. Another body of mass $m$ is hanging as shown in figure. Find the force exerted by the platform on man if $M=50\text{kg},m=10\text{kg}$, Take $g=10{\text{m/s}}^2$.

1. $10\text{N}$
2. $100\text{N}$
3. $25\text{N}$
4. $50\text{N}$

Q. Find the tension in the string.

1. $82.5\text{N}$
2. $95.5\text{N}$
3. $100.2\text{N}$
4. $102\text{N}$

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.

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

1. 8 : 1

2. 9 : 7

3. 4 : 3

4. 5 : 3

Q. In the figure shown, find the velocity of the $3kg$ mass after $10s$ if the system is released from rest at $t=0$. (Take $g=10m/s^2$)

1. $30m/s$
2. $40m/s$
3. $50m/s$
4. $70m/s$

Q. Find the tension in the string between the pulleys and the acceleration of the blocks as shown in the figure. Assume that there is no slipping between the string and the pulleys.
[Given, mass of bigger pulley $=2m$, radius of bigger pulley $=R$, mass of smaller pulley $=m$ and radius of smaller pulley $=\frac{R}{2}$]

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

Q. In the figure given below, with what acceleration (in ${\text{m/s}}^2$) does the block of mass $2m$ move?
(Pulley and strings are massless and frictionless)

1. $\frac{g}{3}$
2. $\frac{2g}{5}$
3. $\frac{2g}{3}$
4. $\frac{7g}{3}$

Q. In the figure shown, find the force exerted by the pulley at the support. Take $g=10{\text{m/s}}^2$ and assume that all surfaces are smooth.

1. $21\text{N}$
2. $42\text{N}$
3. $21\sqrt{2}\text{N}$
4. $\frac{21}{\sqrt{2}}\text{N}$