If the velocity of light c, gravitational constant G and Planck's constant h are chosen as fundamental units, the dimensions of length L in the new system is

• [h¹c¹G^-1]

• [h^1/2c^1/2G^-1/2]

• [h¹c^-3G¹]

• [h^1/2c^-3/2G^1/2]

A plate has a length 5 ± 0.1 cm and breadth 2 ± 0.01 cm. Then the area of the plate is

• 10 ± 0.1 cm²

• 10 ± 0.01 cm²

• 10 ± 0.001 cm²

• 10 ± 1 cm²

A ball hangs from a string inside a train moving along a horizontal straight track. The string is observed to incline towards the rear of the train making a constant small angle with the vertical. It shows that the train is

• moving with a uniform acceleration

• moving with a uniform velocity

• moving with a uniform retardation

• moving with an acceleration which is increasing uniformly

A particle moves along Y-axis in such a way that its y-coordinate varies with time t according to the relation y = 3 + 5t² + 7t². The initial velocity and acceleration of the particle are respectively

• 14 ms^-1 , − 5 ms^-2

• 19 ms^-1 , − 9 ms^-2

• 5 ms^-1 , 14 ms^-2

• 3 ms^-1 , − 5 ms^-2

An object travels north with a velocity of 10 ms^-1 and then speeds up to a velocity of 25 ms^-1 in 5 s. The acceleration of the object in these 5 s is

• 3 ms^-1 in north direction

• 3 ms^-2 in north direction

• 15 ms^-2 in north direction

• 3 ms^-2 in south direction

An automobile in travelling at 50 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 90 km/h, all other conditions remaining same and assuming no skidding, the minimum stopping distance in metres is

• 72

• 92.5

• 102.6

• 129.6

7.

A rifle shoots a bullet with a muzzle velocity of 500 ms^-1 at a small target 50 m away. To hit the target the rifle must be aimed (take g = 10 ms^-2)

• exactly at the target

• 10 cm below the target

• 5 cm above the target

• 5 cm below the target

The centripetal acceleration of particle of mass m moving with a velocity v in a circular orbit of radius r is

• v²/r  along the radius, towards the centre 

• v²/r along the radius, away from the centre 

• mv²/r  along the radius, away from the centre 

• mv²/r  along the radius, towards the centre 

An α-particle of mass m suffers one dimensional elastic collision with a nucleus of unknown mass. After the collision the α-particle is scattered directly backwards losing 75% of its kinetic energy. Then the mass of the nucleus is

• m

• 2m

• 3m

• $\frac{3}{2} \mathrm{m}$

While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of 15° to the horizontal. The speed of the car in km/h is

• 60.5 

• 72.5

• 82.5

• 92.5