A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (vertically). If the acceleration of the system is g/8 then the ratio of the masses is 

1. 8 : 1

2. 9 : 7

3. 4 : 3

4. 5 : 3

A block of mass 4 kg is suspended through two light spring balances A and B. Then A and B will read respectively 

1. 4 kg and zero kg

2. Zero kg and 4 kg

3. 4 kg and 4 kg

4. 2 kg and 2 kg

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. \(\sqrt{2} M g\)
2. \(\sqrt{2} m g\)
3. \(g\sqrt{\left( M + m \right)^{2} + m^{2}}\)
4. \(g\sqrt{\left(M + m \right)^{2} + M^{2}}\)