If C and R denote capacity and resistance, the dimensions of C R are :

• M⁰L⁰T

• ML⁰T

• M⁰L⁰T²

• not expressible in terms of M, L and T

An arrow is shot, its range is 200 m and its time of flight is 5 s. If g =10 m/s², then the horizontal component of velocity of the arrow is :

• 12.5 m/s

• 250 m/s

• 31.25 m/s

• 40 m/s

A force of 49 newtons is just able to move a block of wood weighing 10 kg-on a rough horizontal surface. Its coefficient of friction is :

• 1

• 0.7

• 0.5

• zero

Two bodies of masses m and 2 m have equal kinetic energies. The ratio of their linear momenta is :

• 1

• 1/2

• 1/$\sqrt{2}$

• 2

A ball of mass m elastically collides with a wall with velocity 'v', then change in its momentum is equal to :

• 2m

• 2mv

• + 8mv

• Zero

A solid sphere is rotating about a diameter at an angular velocity ω. If it cools so that its radius reduces to $\frac{1}{\mathrm{n}}$ of its original value, its angular velocity becomes:

• $\frac{\mathrm{\omega }}{\mathrm{n}}$

• $\frac{\mathrm{\omega }}{{\mathrm{n}}^2}$

• nω

• ${\mathrm{n}}^2\mathrm{\omega }$

Two satellites A and B go around a planet P in circular orbits having radius 4 R and R respectively. If the speed of satellite A is 3v, then the speed of satellite B will be

• 6v

• 9v

• 3v

• none of these

The period of oscillation of a simple pendulum of constant length at the surface of the earth is T. Its time period inside a mine will be :

• can not be compared

• equal to T

• less than T

• more than T

When a drop splits up into a number of drops, then :

• Area increases

• Volume increases

• Energy is absorbed

• Energy is liberated

A 5m aluminium wire (Y = 7 × 10¹⁰ N/m²) of diameter 3mm supports a 40 kg mass. In order to have the same elongation in copper wire (Y =12 x 10¹⁰ N/m²) of the same length under the same weight, the diameter should be in mm :

• 1.75

• 2.0

• 2.3

• 5.0