Constrained Motion : General Approach

Q.

In the given situation, two blocks A and B are arranged as shown in the figure. M is a fixed pulley and N is a movable pulley. The system is released from rest. What is the relationship between accelerations for the blocks A and B?

1. a_B = 2a_A

2. a_A = 2a_B

3. a_B = -2a_A

4. a_A = -2a_B

Q. Assuming pulley and string to be ideal and masses to be rigid, calculate the common acceleration of the blocks on smooth surface as shown.

1. $\frac{5-3\sqrt{2}}{16}g$
2. $\frac{5-\sqrt{3}}{16}g$
3. $\frac{5+3\sqrt{2}}{16}g$
4. $\frac{5+\sqrt{3}}{16}g$

Q.

In the arrangement shown in figure find the tensions in the rope and accelerations of the masses $m_1$ and $m_2$ and pulleys $P_1$ and $P_2$ when the system is set free to move. Assume the pulleys to be massless and strings are light and inextensible.

p) T (i) m₁g

q) a₁ (ii) m₂g

r) a₂ (iii) (m₁ - m₂)g

s) ap₁ (iv) g downward

t) ap₂ (v) g upward

(vi) 3g downward

1. p -(ii); q-(v); r- (v); s-(iv); t-(vi)
2. p -(ii); q-(vi); r- (iv); s-(v); t-(iv)
3. p -(i); q-(vi); r- (v); s-(vi); t-(iv)
4. p -(i); q-(iv); r- (iv); s-(vi); t-(iv)

Q.

In the arrangement shown in figure find the tensions in the rope and accelerations of the masses $m_1$ and $m_2$ and pulleys $P_1$ and $P_2$ when the system is set free to move. Assume the pulleys to be massless and strings are light and inextensible.

p) T (i) m₁g

q) a₁ (ii) m₂g

r) a₂ (iii) (m₁ - m₂)g

s) ap₁ (iv) g downward

t) ap₂ (v) g upward

(vi) 3g downward

1. p -(ii); q-(vi); r- (iv); s-(v); t-(iv)

2. p -(i); q-(vi); r- (v); s-(vi); t-(iv)

3. p -(i); q-(iv); r- (iv); s-(vi); t-(iv)

4. p -(ii); q-(v); r- (v); s-(iv); t-(vi)

Q.

Two blocks each of mass M are connected to the ends of a light frame as shown in below figure. The frame is rotated about the vertical line of symmetry. The rod breaks if the tension in it exceeds $T_0$. Find the maximum frequency with which the frame may be rotated without breaking the rod.

1. 

2. 

3. 

4. 

Q. Two blocks of mass m and M are hanging off a single pulley, as shown. Determine the acceleration of the blocks. Ignore the mass of the pulley. m = 1 kg and M = 2 kg, g= 10 $m/s^2$.

1. 5/2
2. 10/3
3. 10
4. 10/7

Q.

Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We conclude that in this position.

1. mg =

2. mg is greater than

3. mg is not greater than

4. mg is not less than

Q.
A conical pendulum has a bob of mass 'm'. As the angular velocity of the bob is inceased such that the bob rotates in a perfect horizontal plane. What will be the tension in the string in this scenario?

1. mg
2. 2mg
3. It is not possible for the bob to spin horizontally
4. 0

Q. Figure shows a hemisphere and a supported rod. Hemisphere is moving right with a uniform velocity $v_2$ and the end of rod which is in contact with ground is moving left with a velocity $v_1$. The rate at which the angle $\theta$ is decreasing will be

1. $\frac{(v_1+v_2){\sin }^2\theta }{R\cos \theta }$
2. $\frac{(v_1+v_2){\cos }^2\theta }{R\sin \theta }$
3. $\frac{(v_1+v_2)\cot \theta }{R\sin \theta }$
4. $\frac{(v_1+v_2)\tan \theta }{R\cos \theta }$

Q. In the given figure, if monkey is accelerating up at 5 m/$s^2$, then acceleration of block on the other side is
(Here the mass of the monkey is 15 kg and mass of the block is 20 kg.)

1. 
   1.25 m/$s^2$ downwards
2. 
   2.5 m/$s^2$ upwards
3. 
   1.25 m/$s^2$ upwards
4. 
   2.5 m/$s^2$ downwards