If the units of length, mass and force are chosen as fundamental units, the dimensions of time would be

• [ M^1/2 L^-1/2 F^1/2 ]

• [ M^1/2 L^1/2 F^1/2 ]

• [ M^1/2 L^1/2 F^-1/2 ]

• [ M^1/2 L^-1/2 F^-1/2 ]

A block of mass 2 kg is placed on the floor. The coefficient of static friction is $0·4$. If a force of $2·8$ N is applied on the block parallel to the floor, the force of friction between the block and the floor is (g = 10 ms^-2 )

• $2·8$ N

• 2 N

• 8 N

• Zero

A heavy truck moving with a velocity of 60 km h^-1 collides with a light drum at rest. If the collision be elastic, then the velocity of the drum immediately after collision will be

• zero

• 60 km h^-1

• 120 km h^-1

• uncertain

A cyclist is moving in a circular track of radius 80 m with a velocity of 36 km h^-1. He has to lean from the vertical approximately through an angle (Take g = 10 m s^-2 )

• tan^-1 (4)

• tan^-1(1/8)

• tan^-1(1/4)

• tan^-1(2)

A satellite is in an orbit around the earth. If its kinetic energy is doubled, then

• it will maintain its path

• it will fall on the earth

• it will rotate with a great speed

• it will escape out of earth's gravitational field

A steel wire with cross-section 3 cm² has elastic limit 2.4 x 10⁸ N m^-2. The maximum upward acceleration that can be given to a 1200 kg elevator supported by this cable wire if the stress is not to exceed one-third of the elastic limit is (Take g = 10 ms^-2)

• 12 m s^-2

• 10 m s^-2

• 8 m s^-2

• 7 m s^-2

An arrow is projected into air. Its time of flight is 5 s and range 200 m. What is the maximum height reached by it? ( Take g= 10 ms^-2 )

• 31·25 m

• 24·5 m

• 18·25 m

• 46·75 m

A particle moves in a circular path with decreasing speed. Choose the correct statement.

• Angular momentum remains constant

• Acceleration $\overrightarrow{\mathrm{\alpha }}$ is towards the centre

• Particle moves in a spiral path with decreasing radius

• The direction of angular momentum remains constant

A body of mass 2 kg is thrown up vertically with kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of its original value is

• 50 m

• 12.25 m

• 25 m

• 10 m

10.

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is

• a

• 2a

• 3a

• none of these