Three weights W, 2W and 3W are connected to identical springs suspended from a rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that 

(1) 3W will be farthest

(2) W will be farthest

(3) All will be at the same distance

(4) 2W will be farthest

When forces F₁, F₂, F₃ are acting on a particle of mass m such that F₂ and F₃ are mutually perpendicular, then the particle remains stationary. If the force F₁ is now removed then the acceleration of the particle is 

(1) $F_1/m$

(2) $F_2{F}_3/m{F}_1$

(3) $(F_2-F_3)/m$

(4) $F_2/m$

Consider the following statement: When jumping from some height, you should bend your knees as you come to rest, instead of keeping your legs stiff. Which of the following relations can be useful in explaining the statement?

1. $\Delta \overrightarrow{p_1}=-\Delta \overrightarrow{p_2}$

2. $\Delta E=-\Delta (PE+KE)=0$

3. $\overrightarrow{F}\Delta t=m\Delta \overrightarrow{v}$

4. $\Delta \overrightarrow{x}\propto \Delta \overrightarrow{F}$

A false balance has equal arms. An object weighs X when placed in one pan and Y when placed in other pan, then the weight W of the object is equal to 

(1) $\sqrt{XY}$

(2) $\frac{X+Y}{2}$

(3) $\frac{X^2+Y^2}{2}$

(4) $\frac{2}{\sqrt{X^2+Y^2}}$ 

In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed 

1. $2U \cos \theta$

2. $U \cos \theta$

3. $\frac{2U}{\cos \theta }$

4. $\frac{U}{\cos \theta }$

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be: 
 
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by:
 
1. \(\sqrt{2} M g\)
2. \(\sqrt{2} m g\)
3. \(g\sqrt{\left( M + m \right)^{2} + m^{2}}\)
4. \(g\sqrt{\left(M + m \right)^{2} + M^{2}}\)

A pulley fixed to the ceilling carries a string with blocks of mass m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with what acceleration 

(1) 0

(2) g/4

(3) g/2

(4) –g/2

A block \(B\) is placed on top of block \(A\). The mass of block \(B\) is less than the mass of block \(A\). Friction exists between the blocks, whereas the ground on which block \(A\) is placed is assumed to be smooth. A horizontal force \(F\), increasing linearly with time begins to act on \(B\). The acceleration \(a_A\) and \(a_B\) of blocks \(A\) and \(B\) respectively are plotted against \(t\). The correctly plotted graph is:

1.		2.
3.		4.

In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t = 2 sec is 

(1) 0.2 kg m sec^–1

(2) –0.2 kg m sec^–1

(3) 0.1 kg m sec^–1

(4) –0.4 kg m sec^–1