Two masses M and M/2 are joint together by means of a light inextensible string passes over a frictionless pulley as shown in figure. When bigger mass is released the small one will ascend with an acceleration of 

(1) g/3

(2) 3g/2

(3) g/2

(4) g

Two masses m₁ and m₂ (m₁ > m₂) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is 

(1) ${\left(\frac{{\displaystyle m_1-m_2}}{{\displaystyle m_1+m_2}}\right)}^{2}g$

(2) $\frac{m_1-m_2}{m_1+m_2}g$

(3) $\frac{m_1+m_2}{m_1-m_2}g$

(4) Zero

The mass of a body measured by a physical balance in a lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as:

(1) $m\left(1-\frac{{\displaystyle a}}{{\displaystyle g}}\right)$

(2) $m\left(1+\frac{{\displaystyle a}}{{\displaystyle g}}\right)$

(3) m

(4) Zero

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) $F_2/m$

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) $\frac{2}{\sqrt{X^2+Y^2}}$ 

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. $\sqrt{2}Mg$

2. $\sqrt{2}mg$

3. $\sqrt{{(M+m)}^2+m^2}g$

4.$\sqrt{{(M+m)}^2+M^2}g$

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.