Constrained Motion : General Approach

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:

1. $v$
2. $\frac{v}{\sin \theta }$
3. $v\sin \theta$
4. $\frac{v}{\cos \theta }$

Q. A fish rising vertically up towards the surface of water with speed $3{\text{ms}}^{-1}$ observes a bird diving vertically down towards it with speed $9{\text{ms}}^{-1}$. The actual velocity of the bird is

1. $4.5{\text{ms}}^{-1}$
2. $5.4{\text{ms}}^{-1}$
3. $3.0{\text{ms}}^{-1}$
4. $3.4{\text{ms}}^{-1}$

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

1. $-3\text{J/kg}$
2. $-12\text{J/kg}$
3. $-5\text{J/kg}$
4. None of these

Q. Block $B$ moves to the right with a constant velocity $v_0.$ 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

1. $\frac{v_0}{2},$ towards left
2. $\frac{v_0}{2},$ towards right
3. $\frac{3v_0}{2},$ towards left
4. $\frac{3v_0}{2},$ 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 $v_A$, speed and acceleration of block B at the instant is $v_B$ and $a_B$ respectively, which of the following option(s) is/are correct?

1. $v_B=v_A,a_B=0$
2. $a_B=0$
3. $v_B=\frac{3}{5}{v}_A$
4. $a_B=\frac{16v_A^2}{125}$

Q. Calculate the acceleration of the block $B$ in the shown figure, assuming the surfaces and the pulleys $p_1$ and $p_2$ are smooth and the string is light.

1. $\frac{3F}{17m}m/s^2$
2. $\frac{2F}{17m}m/s^2$
3. $\frac{3F}{15m}m/s^2$
4. $\frac{3F}{12m}m/s^2$

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

1. $1.8\text{m/s}$ in downward direction
2. $1.8\text{m/s}$ in upward direction
3. $0.6\text{m/s}$ in downward direction
4. $0.6\text{m/s}$ 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 $\frac{g}{4}$ relative to the rope. The tension in the rope is (take g = 10 $m{s}^{-2}$)

1. 

2. 

3. 

4. 

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

1. $2a_1+a_2+a_3=0$
2. $a_1+2a_2+a_3=0$
3. $a_1+a_2+2a_3=0$
4. $-2a_1+a_2+a_3=0$

Q. The pulley and strings shown in the figure below are massless. Find the Acceleration of system.
(Take $g=10{\text{m/s}}^2$)

1. $2{\text{m/s}}^2$
2. $1{\text{m/s}}^2$
3. $1.5{\text{m/s}}^2$
4. $2.5{\text{m/s}}^2$

Q.

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

1. $15\text{m/s}$ (Downward)
2. $15\text{m/s}$ (Upward)
3. $10\text{m/s}$ (Downward)
4. $10\text{m/s}$ (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 $v_2$ 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.

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 $5\text{m/s}$ after it has moved $5\text{m}$ 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 $g=10m/s^2$)

1. $100\text{N}$
2. $96\text{N}$
3. $50\text{N}$
4. $75\text{N}$

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 $g=10\frac{m}{s^2})$

1. Acceleration of block A is 1 $\frac{m}{s^2}$
2. Acceleration of block A is 2 $\frac{m}{s^2}$
3. Tension in string connected to block B is 40 N
4. Tension in string connected to block B is 80 N

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

1. $-\frac{L^2{v}_A^2}{{(L^2-y^2)}^{3/2}}$
2. $-\frac{L{v}_A^2}{{(L^2-y^2)}^{3/2}}$
3. $-\frac{L^2{v}_A^2}{{(L-y)}^3}$
4. $-\frac{L^2{v}_A}{{(L^2-y^2)}^{3/2}}$

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.

1. $25\text{m/s}$
2. $20\text{m/s}$
3. $22\text{m/s}$
4. $30\text{m/s}$

Q. System is shown in the figure and man is pulling the rope from both sides with constant speed $‘u^{\prime }$. Then what will be the velocity of the block, if the rope is inextensible?

1. $\frac{3u}{4}$
2. $\frac{u}{2}$
3. $\frac{u}{4}$
4. $u$

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

2. $1.5\times {10}^{5}J$

3. $1.05\times {10}^{5}J$

4. The information is given insufficient

Q. If acceleration of block $A$ is $2{\text{m/s}}^2$ to left and acceleration of block $B$ is $1{\text{m/s}}^2$ to left, then what will be the acceleration of block $C$? Assume that the surface and pulleys are smooth and string is inextensible.

1. $1{\text{m/s}}^2$ upwards
2. $1{\text{m/s}}^2$ downwards
3. $2{\text{m/s}}^2$ downwards
4. $2{\text{m/s}}^2$ upwards

Q. In the given constraint, if the string is inextensible and pulley is frictionless, then magnitude of velocity of block $A$ $\left(V_A\right)$ is

1. $20\text{m/s}$
2. $5\text{m/s}$
3. $10\text{m/s}$
4. $15\text{m/s}$

Q. In the figure shown below, acceleration of block $A$ is $1{\text{m/s}}^2$ upwards, acceleration of block $B$ is $7{\text{m/s}}^2$ upwards and acceleration of block $C$ is $2{\text{m/s}}^2$ upwards. Then what will be the acceleration of block $D$? Assume that the pulleys are frictionless and strings are inextensible.

1. $7{\text{m/s}}^2$ upwards
2. $2{\text{m/s}}^2$ downwards
3. $10{\text{m/s}}^2$ downwards
4. $8{\text{m/s}}^2$ upwards

Q. In the given constraint, if the pulley is frictionless and the string is inextensible, then velocity of block $B$ $\left(V_B\right)$ is

1. $10\text{m/s}$
2. $15\text{m/s}$
3. $20\text{m/s}$
4. $25\text{m/s}$

Q. Assuming the string to be inextensible and surface and pulley to be frictionless, velocity of block $B$ $\left(V_B\right)$ in the given figure is

1. $2\text{m/s}$
2. $10\text{m/s}$
3. $6\text{m/s}$
4. $8\text{m/s}$

Q. Two blocks are arranged as shown in the figure. What will be the relation between the accelerations $a_1$ of block $m_1$ and $a_2$ of block $m_2$, if the surface and the pulleys are frictionless and the strings are inextensible?

1. $a_1$= $a_2$
2. $a_1=6$$a_2$
3. $a_1=3$$a_2$
4. $a_1=4$$a_2$

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

1. $200m/s$

2. $220m/s$

3. $240m/s$

4. $260m/s$

Q. Two sliders $A$ and $B$ connected by a light rigid rod $10\text{m}$ 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 $\text{m/s}$ upto two decimals) when $x=6\text{m}$. Assume $m_A=m_B=200\text{kg}$ and $m_c=100\text{kg},\sqrt{\frac{2}{33}}=0.25$.

Q. Determine the relationship that governs the velocities of four cylinders if $v_A$, $v_B$, $v_C$ and $v_D$ represents velocities of block A, B, C and D. Consider downward velocity as positive and strings inextensible.

1. $4v_A+8v_B-4v_C+v_D=0$
2. $4v_A+8v_B+4v_C+v_D=0$
3. $4v_A-8v_B+4v_C-v_D=0$
4. $-4v_A+8v_B-4v_C+v_D=0$

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?

1. $6m/s$
2. $4m/s$
3. $0m/s$
4. None of these