Physics Test 193

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Physics Test 193

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Question 1
4 / -1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

A
the linear momentum of 5 remains constant in magnitude.

B
the acceleration of S is always directed towards the centre of the earth.

C
the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.

D
the total mechanical energy of S varies periodically with time.

Solution

The gravitational force on the satellite S acts towards the centre of the earth, so the acceleration of the satellite S is always directed towards the centre of the earth.
Question 2
4 / -1

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 × 10²⁴kg) have to be compressed to be a black hole?

A
10⁻⁹ m

B
10⁻⁶ m

C
10⁻² m

D
100 m

Solution
Question 3
4 / -1

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m ,..., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

A
−4/3G

B
−4G

C
−G

D
−8/3G

Solution

The resulting gravitational potential at the origin O due to each of mass 2 kg located at positions as shown in figure is
Question 4
4 / -1

The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. V_P and V_E are escape velocities of the planet and the earth, respectively, then

A
V_P = 1.5V_E

B
V_P = 2V_E

C
V_E = 3V_P

D
V_E = 1.5V_P

Solution
Question 5
4 / -1

The height at which the weight of a body becomes 1/16th its weight on the surface of earth (radius R), is

A
5 R

B
15 R

C
3 R

D
4 R

Solution
Question 6
4 / -1

The total mechanical energy of a spring-mass system in simple harmonic motion is E = 1/2mω²A². Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will

A
become 2E

B
become E/2

C
become √2E

D
remain E

Solution

Total energy depends on k of spring and amplitude A. It is independent of mass.
Question 7
4 / -1

A body describes simple harmonic motion with an amplitude of 5 cm, and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 3 cm, and when the displacement is zero.

A

B

C

D

Solution
Question 8
4 / -1

A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph

A

B

C

D

Solution

Potential energy of particle performing SHM varies parabolically in such a way that at mean position it becomes zero and maximum at extreme position.
Question 9
4 / -1

Two simple harmonic motions of angular frequency 100 and 1000 rad s^–1 have the same displacement amplitude. The ratio of their maximum acceleration is

A
1 : 10³

B
1 : 10⁴

C
1 : 10

D
1 : 10²

Solution
Question 10
4 / -1

The displacement of a particle along the x-axis is given by x = asin²ωt. The motion of the particle corresponds to

A
Simple harmonic motion of frequency ω/π

B
Simple harmonic motion of frequency 3ω/2π

C
Non simple harmonic motion

D
Simple harmonic motion of frequency ω/2π

Solution