A uniform rod of length $200 \text{ cm}$ and mass $500 \text{ g}$ is balanced on a wedge placed at $40 \text{ cm}$ mark. A mass of $2 \text{ kg}$ is suspended from the rod at $20 \text{ cm}$ and another unknown mass '$m$' is suspended from the rod at $160 \text{ cm}$ mark as shown in the figure. Find the value of '$m$' such that the rod is in equilibrium. ($g = 10 \text{ m/s}^2$)

A capacitor of capacitance $C = 900 \text{ pF}$ is charged fully by $100 \text{ V}$ battery $B$ as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance $C = 900 \text{ pF}$ as shown in figure (b). The electrostatic energy stored by the system (b) is

Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as:

A block A of mass $m_1$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block B of mass $m_2$ is suspended. The coefficient of kinetic friction between block A and the table is $\mu_k$. When block A is sliding on the table, the tension in the string is:

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its height if the air resistance is not ignored?

A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s$^{-1}$. If the vertical component of earth's magnetic field at that place is $2 \times 10^{-5}$ T and electrical resistance of the coil is 12.56 $\Omega$, then the maximum induced current in the coil will be

A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rd second?

The velocity of a bullet is reduced from $200 \text{ m/s}$ to $100 \text{ m/s}$ while travelling through a wooden block of thickness $10 \text{ cm}$. The retardation, assuming it to be uniform, will be:

A body A starts from rest with an acceleration $a_1$. After $2$ seconds, another body B starts from rest with an acceleration $a_2$. If they travel equal distances in the $5^{\text{th}}$ second, after the start of A, then the ratio $a_1 : a_2$ is equal to: