Constrained Motion : Intuitive Approach

Q.

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

1. 1 m/s

2. 

3. 

4. 

Q. Velocity of block B in the given arrangement is $300mm/sec$ towards right. Then velocity of A will be

1. $200mm/sec$
2. $100mm/sec$
3. $450mm/sec$
4. $150mm/sec$

Q. Find the value of acceleration of block $B$ (in ${\text{m/s}}^2$) for the system shown in figure. Take $g=10{\text{m/s}}^2$.

1. $\frac{15}{2}{\text{m/s}}^2$
2. $\frac{5}{2}{\text{m/s}}^2$
3. $8{\text{m/s}}^2$
4. $\frac{25}{2}{\text{m/s}}^2$

Q.

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4 m/s due east. The river is 800 m wide. What is his velocity relative to the earth? Assume North as positive y-direction.

1. 

2. 

3. 

4. 

Q.

If $\overrightarrow{A}$ = 2 $\hat{i}$ + 3$\hat{j}$ - $\hat{k}$ and $\overrightarrow{B}$ = -$\hat{i}$ + 3$\hat{j}$ + 4$\hat{k}$ then find the projection of

$\overrightarrow{A}$ on $\overrightarrow{B}$

1. 

2. 

3. None of these

4. 25

Q.

Pulley - massless, frictionless String - massless Wedge-frictionless In the figure find the acceleration of the blocks if the wedge is fixed.

1. rightwards

2. rightwards

3. none of these

4. leftwards

Q.

Mass of wedge as shown in figure is M and that of the block is m. Neglecting friction at all the places and mass of the pulley, calculate acceleration of the wedge. Thread is inextensible.

1. $\frac{mgsin\theta }{M+m(1-cos\theta )}$

2. $\frac{mgsin\theta }{M+2m(1-cos\theta )}$

3. $\frac{M+m(1-cos\theta )g}{msin\theta }$

4. mg sin$\theta$

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. Find the velocity of block C.

Q. If the block $\text{B}$ moves towards right with acceleration $\text{b}$, then the net acceleration of block $\text{A}$ is

1. $b\hat{i}+4b\hat{j}$
2. $b\hat{i}+b\hat{j}$
3. $b\hat{i}+2b\hat{j}$
4. None of these

Q. What will be the velocity of block A in the arrangement shown ?

1. $60m/s$
2. $120m/s$
3. $140m/s$
4. $200m/s$

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.

A shell acquires the initial velocity $v$ = 320 m/s, having made $n$ = 2.0 turns inside the barrel whose length is equal to $l$ = 2.0 m. Assuming that the shell moves inside the barrel with a uniform acceleration, find the angular velocity of its axial rotation, at the moment when the shell escapes the barrel.

1. Data insufficient

2. 

3. 

4. 

Q. A thin circular loop of radius R rotates about its vertical diameter with an angular frequency $\omega$. Show that a small bead on the wire loop remains at its lower most point for $\omega \le \sqrt{g/R}$. What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for $\omega =\sqrt{2g/R}$ ? Neglect friction.

Q. A small block of mass $m$ rests on a smooth wedge of angle $\theta$. With what horizontal acceleration $a$ should the wedge be pulled, as shown in the figure, so that the block falls freely.

1. $g\cos \theta$
2. $g\sin \theta$
3. $g\cot \theta$
4. $g\tan \theta$

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. 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.

The friction coefficient between the two blocks shown in figure is $\mu$ but the floor is smooth. Assume the entire system is kept inside an elevator coming down with an acceleration a < g.

1. 2m(g-a),

2. 2m(g-a),

3. 2,

4. None of these