Constrained Motion : Intuitive Approach

Q.

Find velocity of ring B ($V_B$) at an instant as shown. The string is taut and inextensible:

1. $\frac{1}{2}m/s$

2. $\frac{\sqrt{3}}{4}m/s$

3. $\frac{1}{4}m/s$

4. 1 m/s

Q.

A block of mass 2 kg slides down the face of a smooth ${45}^{\circ }$ wedge of mass 9kg as shown in figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge.

1. 2 m/$s^2$.

2. $\frac{11}{\sqrt{2}}$ m/$s^2$.

3. 1 m/$s^2$.

4. none of these

Q. Find out the velocity of block $E$ for the arrangement as shown in figure. Consider all pulleys to be light and frictionless. All surfaces are smooth and the string is massless and inextensible.

1. $\frac{21}{2}\text{m/s}$ (upwards)
2. $\frac{31}{2}\text{m/s}$ (downwards)
3. $\frac{31}{2}\text{m/s}$ (upwards)
4. $\frac{21}{2}\text{m/s}$ (downwards)

Q. An arrangement of pulley, string and blocks is shown in figure. Given $m_1=4\text{kg},m_2=2\text{kg}$ and $m_3=4\text{kg}$. All surfaces are frictionless, string and pulleys are massless. Find the acceleration of block $m_1$. Assume $g=10{\text{m/s}}^2$.

1. $\frac{36}{11}{\text{m/s}}^2$
2. $\frac{40}{11}{\text{m/s}}^2$
3. $\frac{36}{7}{\text{m/s}}^2$
4. $\frac{40}{7}{\text{m/s}}^2$

Q. Velocities of blocks $A,B$ and pulley $P_2$ are shown in the figure given below, then

1. Velocity of pulley $P_1$ will be $5\text{m/s}$ downwards.
2. Velocity of block $C$ will be $25\text{m/s}$ upwards.
3. Velocity of pulley $P_1$ will be $5\text{m/s}$ upwards.
4. Velocity of block $C$ will be $15\text{m/s}$ downwards.

Q.

In each of the three arrangements, the block of mass m₁ is being pulled left with constant velocity. All surfaces are smooth. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass $m_2$ in the three cases respectively is:

1. 2 : 1 : 4

2. 2 : 4 : 1

3. 4 : 2 : 1

4. can not be calculated

Q. Masses $M_1,M_2$ and $M_3$ are connected by strings of negligible mass which pass over massless and frictionless pulleys $P_1$ and $P_2$ as shown in fig. The masses move such that the portion of the string between $P_1$ and $P_2$ is parallel to the inclined plane and the portion of the string between $P_2$ and $M_3$ is horizontal. The masses $M_2$ and $M_3$ are $4.0kg$ each and the coefficient of kinetic friction between the masses and the surface is $\mathrm{0.25.}$ The inclined plane makes an angle of ${37}^{\circ }$ with the horizontal. If the mass $M_1$ moves downwards with a uniform velocity. find the mass of $M_1$ in $\text{kg}$.

Q. In the figure, assume that there is negligible friction between the blocks and the table. Compute the acceleration of $m_1$ in $m/s^2$, if acceleration of $m_2$ due to force $F$ is $5m/s^2$ and $m_1=300g,m_2=200g$

Q. In the figure, assume that there is negligible friction between the blocks and the table. Compute the acceleration of $m_1$ in $m/s^2$, if acceleration of $m_2$ due to force $F$ is $5m/s^2$ and $m_1=300g,m_2=200g$

Q. Three blocks $\text{a, b and c}$ of masses $10kg$, $10kg$ and $20kg$ respectively are arranged as shown in figure. All the surfaces are frictionless and string is inextensible. A constant force $F=20N$ is applied on block $\text{a}$ as shown. Pulley and string are light. Part of the string connecting both pulleys is vertical and part of the strings connecting pulleys with masses a and b are horizontal. Choose the correct option(s) for the given system.

1. Acceleration of block b is $0.5m/s^2$
2. Acceleration of block $\text{b}$ is $1m/s^2$
3. Tension in the string is $10N$
4. Acceleration of block $\text{c}$ is $0.5m/s^2$

Q. Three blocks $\text{a, b and c}$ of masses $10kg$, $10kg$ and $20kg$ respectively are arranged as shown in figure. All the surfaces are frictionless and string is inextensible. A constant force $F=20N$ is applied on block $\text{a}$ as shown. Pulley and string are light. Part of the string connecting both pulleys is vertical and part of the strings connecting pulleys with masses a and b are horizontal. Choose the correct option(s) for the given system.

1. Acceleration of block b is $0.5m/s^2$
2. Acceleration of block $\text{b}$ is $1m/s^2$
3. Tension in the string is $10N$
4. Acceleration of block $\text{c}$ is $0.5m/s^2$

Q.

A block of mass 2 kg slides down the face of a smooth ${45}^{\circ }$ wedge of mass 9kg as shown in figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge.

1. 2 m/$s^2$.

2. $\frac{11}{\sqrt{2}}$ m/$s^2$.

3. 1 m/$s^2$.

4. none of these

Q. In the arrangement shown in figure, the relation between acceleration of blocks $m_1$ and $m_2$ is

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

Q. Find the velocity of 'B' if the end of the rope is pulled with a speed of $1\text{m/s}$.
(Given that '$B$' is constrained to move along vertical)

1. $\frac{1}{2}\text{m/s}$
2. $\frac{1}{3}\text{m/s}$
3. $\frac{3}{4}\text{m/s}$
4. $\frac{3}{8}\text{m/s}$

Q. Find out the velocity of block $E$ for the arrangement as shown in figure. Consider all pulleys to be light and frictionless. All surfaces are smooth and the string is massless and inextensible.

1. $\frac{21}{2}\text{m/s}$ (upwards)
2. $\frac{31}{2}\text{m/s}$ (downwards)
3. $\frac{31}{2}\text{m/s}$ (upwards)
4. $\frac{21}{2}\text{m/s}$ (downwards)

Q. A block A of mass $5\text{kg}$ is placed on a table and connected to another block B of mass $3\text{kg}$ with a light string passing over a frictionless pulley. The coefficient of friction between the table the block A is $0.4$. The block B is suddenly dropped and the string breaks after $3$ seconds. What is the total distance covered by block A?

1. $5.625\text{m}$
2. $1.75\text{m}$
3. $7.375\text{m}$
4. $6.5\text{m}$

Q. Both springs, string and pulley shown in the figure are light. Initially when both the springs were in their natural state, the system was released from rest. The maximum displacement of the block having mass $m$ is:

1. $\frac{5mg}{k}$
2. $\frac{3mg}{k}$
3. $\frac{10mg}{k}$
4. $\frac{4mg}{k}$

Q. In figure shown, velocity of mass $m$ at the moment shown is $U$. Find the velocity of the ring along the rod if it can slide along the smooth rod.

1. $\frac{U}{2}$
2. $2U$
3. $\frac{2U}{\sqrt{3}}$
4. $\frac{\sqrt{3}U}{2}$