If C is the capacitance and V is the potential, the dimensional formula for CV² is

• [ML²T^-1]

• [ML^-2T^-3]

• [ML²T^-2]

• [ML^-2T^-2]

An object is dropped from rest. Its v-t graph is

A particle starts from rest at t = 0 and moves in a straight line with an acceleration as shown in figure. The velocity of the particle at t = 3 s is

• 2 ms^-1

• 4 ms^-1

• 6 ms^-1

• 8 ms^-1

Two cars A and B are moving with same speed of 45 km/h along same direction. If a third car C coming from the opposite direction with a speed of 36 km/h meets two cars in an interval of 5 min, the distance of separation of two cars A and B should be (in km)

• 6.75

• 7.25

• 5.55

• 8.35

Two particles A and B are projected with same speed so that the ratio of their maximum heights reached is 3 : 1. If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is

• 1 : 1

• 2 : 1

• 4 : 1

• 3 : 2

An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of 0.25 ms^-2 is (g = 10 ms^-2)

• 51.25 N

• 48.75 N

• 52.75 N

• 47.25 N

A particle  acted upon by constant forces $4\hat{\mathrm{i}} + \hat{\mathrm{j}} - 3\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}$ is displaced from the point $\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ to the point $5\hat{\mathrm{i}} + 4\hat{\mathrm{j}} + \hat{\mathrm{k}}$. The total work done by the forces in SI unit is

• 20

• 40

• 50

• 30

Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg-wt. If they acquire the same kinetic energy in times t_A and t_B, then the ratio $\frac{{\mathrm{t}}_{\mathrm{A}}}{{\mathrm{t}}_{\mathrm{B}}}$ is

• $\frac{1}{2}$

• 2

• $\frac{2}{5}$

• $\frac{5}{6}$

A bullet of mass 0.05 kg moving with a speed of 80 ms enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the below is

• 300 N

• 20 N

• 400 N

• 40 N

A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below.

The velocity of the particle after 10 s is

• 20 ms^-1

• 10 ms^-1

• 50 ms^-1

• 26 ms^-1