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) $F_2/m$

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. $\frac{U}{\cos \theta }$