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JEE Physics Solved Question Paper 2003

Multiple Choice Questions

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

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

9.
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

$\frac{3}{2} m$

$\frac{1}{2} m_{1} {u_{1}}^{2} - \frac{1}{2} m_{1} {v_{1}}^{2} = \frac{75}{100} \times \frac{1}{2} m_{1} {u_{1}}^{2} \Rightarrow {u_{1}}^{2} - {v_{1}}^{2} = \frac{3}{4} {u_{1}}^{2} \Rightarrow v_{1} = \frac{1}{2} u_{1} . . . . . . . . (i) Now, v_{1} = \frac{(m_{2} - m_{1})}{(m_{1} + m_{2})} . . . . . . . . (ii) Thus, \frac{1}{2} u_{1} = \frac{(m_{2} - m_{1}) u_{1}}{(m_{1} + m_{2})} \Rightarrow m_{2} = 3 m_{1} = 3 m$

10.

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