$A$ frictionless pulley is attached to one arm of a balance and a string passed around it carries two masses $m_1$ and $m_2$. The pulley is provided with a clamp due to which $m_1$ and $m_2$ do not move with respect to each other. On removing the clamp,$m_1$ and $m_2$ start moving. How much change in counter mass has to be made to restore balance?

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the center $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$ is

The ends of a rope are held by two men who pull on it with equal and opposite forces of magnitude $F$ each. Then the tension in the rope is

Two identical blocks each of mass $M$ are attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. $A$ small mass $m$ is now placed on block $B$ (the right block). The acceleration with which the two blocks move together is ($g =$ gravitational acceleration).

$A$ lift is going up. The total mass of the lift and the passenger is $1500\, kg$. The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at $t = 11\, s$ will be ............ $N$.

If the mass of block $B$ is $3\,kg$ and the mass of block $A$ is $7\,kg$,then the acceleration of the system is ........... $m/s^2$. $(g = 10\,m/s^2)$