If C be the capacitance and V be the electric potential, then the dimensional formula of CV² is

• [ML²T^-2A⁰]

• [MLT^-2A^-1]

• [M⁰LT^-2A⁰]

• [ML^-3TA]

The displacement-time graph of two moving particles make angles of 30° and 45° with the X-axis. The ratio of their velocities is

• $\sqrt{3} : 2$

• 1 : 1

• 1 : 2

• $1 : \sqrt{3}$

Block A of mass of 2 kg is placed over block B of mass 8 kg. The combination is placed over a rough horizontal surface. Coefficient of friction between B and the floor is 0.5. Coefficient of friction between blocks A and B is 0.4. A horizontal force of 10 N is applied on block B. The force of friction between blocks A and Bi s (g = 10 ms^-2)

• 100 N

• 40 N

• 50 N

• Zero

The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = 8t − 5t² m and x = 6t m, where t is in seconds. The velocity with which the projectile is projected is

• 6 ms^-1

• 8 ms^-1

• 10 ms^-1

• 14 ms^-1

A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity = 9.8 ms^-2)

• 5 m

• 2.5 m

• 10 m

• 12.5 m

A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is

• $\frac{1}{2} {\mathrm{mv}}^2$

• $\frac{5}{3} {\mathrm{mv}}^2$

• $\frac{2}{5} {\mathrm{mv}}^2$

• $\frac{7}{10} {\mathrm{mv}}^2$

Two satellites of mass m and 9m are orbiting a planet in orbits of radius R. Their periods of revolution will be in the ratio of

• 9 : 1

• 3 : 1

• 1 : 1

• 1 : 3

The resultant of two forces acting at an angle of 120° is 10 kg-wt and is perpendicular to one of the forces. That force is

• $10\sqrt{3} \mathrm{kg}-\mathrm{wt}$

• $20\sqrt{3} \mathrm{kg}-\mathrm{wt}$

• 10 kg-wt

• $\frac{10}{\sqrt{3}} \mathrm{kg}-\mathrm{wt}$

Faintest stars are called

• zero magnitude stars

• second magnitude stars

• sixth magnitude stars

• dwarfs

The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension,when the same tension is applied ?

• L = 1000 cm, r = 0.2 mm

• L = 2000 cm, r = 0.4 mm

• L = 3000 cm, r = 0.6 mm

• L = 4000 cm, r = 0.8 mm