# Constrained Motion : General Approach

## Trending Questions

**Q.**A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in figure. The horizontal velocity of the block is:

- v
- vsinθ
- vsinθ
- vcosθ

**Q.**A fish rising vertically up towards the surface of water with speed 3 ms−1 observes a bird diving vertically down towards it with speed 9 ms−1. The actual velocity of the bird is

- 4.5 ms−1
- 5.4 ms−1
- 3.0 ms−1
- 3.4 ms−1

**Q.**A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m/s as it reached A. The work done by the person on the mass is −3 J. The potential at A is

- −3 J/kg
- −12 J/kg
- −5 J/kg
- None of these

**Q.**Block B moves to the right with a constant velocity v0. Assuming the pulleys and the surface to be smooth and the string to be inextensible, the velocity of block A relative to block B is

- v02, towards left
- v02, towards right
- 3v02, towards left
- 3v02, towards right

**Q.**The string shown in the figure is passing over a small smooth pulley rigidly attached to trolley A. If the speed of the trolley is constant and equal to vA, speed and acceleration of block B at the instant is vB and aB respectively, which of the following option(s) is/are correct?

- vB=vA, aB=0
- aB=0
- vB=35vA
- aB=16v2A125

**Q.**Calculate the acceleration of the block B in the shown figure, assuming the surfaces and the pulleys p1 and p2 are smooth and the string is light.

- 3F17m m/s2
- 2F17m m/s2
- 3F15m m/s2
- 3F12m m/s2

**Q.**If block A has a velocity of 0.6 m/s to the right, determine the velocity of block B. Assume that the surface is frictionless and the string is inextensible.

- 1.8 m/s in downward direction
- 1.8 m/s in upward direction
- 0.6 m/s in downward direction
- 0.6 m/s in upward direction

**Q.**

In order to raise a mass of 100 kg, a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with acceleration 5 g4 relative to the rope. The tension in the rope is (take g = 10 ms−2)

**Q.**Find the constraint relation between acceleration of block 1, 2 and 3.

- 2a1+a2+a3=0
- a1+2a2+a3=0
- a1+a2+2a3=0
- −2a1+a2+a3=0

**Q.**The pulley and strings shown in the figure below are massless. Find the Acceleration of system.

(Take g=10 m/s2)

- 2 m/s2
- 1 m/s2
- 1.5 m/s2
- 2.5 m/s2

**Q.**

At a given instant, block A is moving with velocity of 5 m/s upwards. What is the velocity of block B at that time?

- 15 m/s (Downward)
- 15 m/s (Upward)
- 10 m/s (Downward)
- 10 m/s (Upward)

**Q.**

A car of mass 2000 kg is lifted up a distance of 30 m by a crane in 1 minute. A second crane does the same job in 2 minutes. Do the cranes consume the same or different amounts

of fuel? What is the power supplied by each crane? Neglect power dissipation against friction.

Take g = 10 ms^{–2}.

**Q.**Figure shows a hemisphere and a supported rod. Hemisphere is moving right with a uniform velocity v2 and the end of rod which is in contact with ground is moving left with a velocity v1. The rate at which the angle θ is decreasing will be

- (v1+v2)sin2θRcosθ
- (v1+v2)cos2θRsinθ
- (v1+v2)cotθRsinθ
- (v1+v2)tanθRcosθ

**Q.**

An aeroplane on a runway, starts from rest and picks up a velocity of 180 km/h and takes off. In doing so, it covers a runway of 1.5 km. Calculate the time in which it takes off?

**Q.**The system starts from rest and block A attains a velocity of 5 m/s after it has moved 5 m towards the right. Assuming the arrangement to be frictionless everywhere and pulley & strings to be light, find the value of the constant force F applied on block A. (Take g=10 m/s2)

- 100 N
- 96 N
- 50 N
- 75 N

**Q.**Figure shows two blocks A and B connected to an ideal pulley string system. In this system when bodies are released then: (neglect friction and take g=10ms2)

- Acceleration of block A is 1 ms2
- Acceleration of block A is 2 ms2
- Tension in string connected to block B is 40 N
- Tension in string connected to block B is 80 N

**Q.**Collars A and B slide along the fixed right-angle rods and are connected by a cord of length L. Determine the acceleration of collar B as a function of y if collar A is given a constant upward velocity vA.

- −L2v2A(L2−y2)3/2
- −Lv2A(L2−y2)3/2
- −L2v2A(L−y)3
- −L2vA(L2−y2)3/2

**Q.**Find velocity of block B at the instant shown in figure. Assume the surface and pulleys to be frictionless and string to be inextensible.

- 25 m/s
- 20 m/s
- 22 m/s
- 30 m/s

**Q.**System is shown in the figure and man is pulling the rope from both sides with constant speed ‘u′. Then what will be the velocity of the block, if the rope is inextensible?

- 3u4
- u2
- u4
- u

**Q.**

A car weighing $500kg$.working against the resistance of $500N$ accelerates from rest to $20\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{${s}^{-1}$}\right.$ in $100m$.$\left(g=10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{${s}^{2}$}\right.\right).$The work done by the engine of the car is

$1.0\times {10}^{5}J$

$1.5\times {10}^{5}J$

$1.05\times {10}^{5}J$

The information is given insufficient

**Q.**If acceleration of block A is 2 m/s2 to left and acceleration of block B is 1 m/s2 to left, then what will be the acceleration of block C? Assume that the surface and pulleys are smooth and string is inextensible.

- 1 m/s2 upwards
- 1 m/s2 downwards
- 2 m/s2 downwards
- 2 m/s2 upwards

**Q.**In the given constraint, if the string is inextensible and pulley is frictionless, then magnitude of velocity of block A (VA) is

- 20 m/s
- 5 m/s
- 10 m/s
- 15 m/s

**Q.**In the figure shown below, acceleration of block A is 1 m/s2 upwards, acceleration of block B is 7 m/s2 upwards and acceleration of block C is 2 m/s2 upwards. Then what will be the acceleration of block D? Assume that the pulleys are frictionless and strings are inextensible.

- 7 m/s2 upwards
- 2 m/s2 downwards
- 10 m/s2 downwards
- 8 m/s2 upwards

**Q.**In the given constraint, if the pulley is frictionless and the string is inextensible, then velocity of block B (VB) is

- 10 m/s
- 15 m/s
- 20 m/s
- 25 m/s

**Q.**Assuming the string to be inextensible and surface and pulley to be frictionless, velocity of block B (VB) in the given figure is

- 2 m/s
- 10 m/s
- 6 m/s
- 8 m/s

**Q.**Two blocks are arranged as shown in the figure. What will be the relation between the accelerations a1 of block m1 and a2 of block m2, if the surface and the pulleys are frictionless and the strings are inextensible?

- a1= a2
- a1=6a2
- a1=3a2
- a1=4a2

**Q.**

A body of $5kg$ is moving with a velocity of $20m/s$. If a force of $100N$is applied on it for $10s$ in the same direction as its velocity, what will now be the velocity of the body

$200m/s$

$220m/s$

$240m/s$

$260m/s$

**Q.**Two sliders A and B connected by a light rigid rod 10 m long, move in two frictionless shafts as shown in the figure. If B starts from O and is at rest initially, determine the velocity of B ( in m/s upto two decimals) when x=6 m. Assume mA=mB=200 kg and mc=100 kg, √233=0.25.

**Q.**Determine the relationship that governs the velocities of four cylinders if vA, vB, vC and vD represents velocities of block A, B, C and D. Consider downward velocity as positive and strings inextensible.

- 4vA+8vB−4vC+vD=0
- 4vA+8vB+4vC+vD=0
- 4vA−8vB+4vC−vD=0
- −4vA+8vB−4vC+vD=0

**Q.**In the figure given below, velocities of different blocks are shown. What will be the speed of block C, if pulleys are frictionless and strings are inextensible?

- 6 m/s
- 4 m/s
- 0 m/s
- None of these