Physics Test 167

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Physics Test 167

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Question 1
4 / -1

A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude :

A
1/2 sec

B
1/3 sec

C
1/4 sec

D
1/6 sec

Solution
Question 2
4 / -1

A horizontal rod of mass m and length L is pivoted smoothly at one end. The rod ’s other end is supported by a spring of force constant k. The rod is rotated (in vertical plane) by a small angle q from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is :

A

B

C

D

Solution

(torque due to mg was already balanced so it is not taken in calculation)
Question 3
4 / -1

A traveling wave y = A sin (kx - ωt + θ) passes from a heavier string to a lighter string. The reflected wave has amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is:

A

B

C

D

Solution

As wave has been reflected from a rarer medium,therefore there is no change in phase.Hence equation for the opposite direction can be written as:

y = 0.5A sin (-kx - ωt + θ) = -0.5A sin (kx + ωt - θ)
Question 4
4 / -1

A string of length 1.5 m with its two ends clamped is vibrating in fundamental mode. Amplitude at the centre of the string is 4 mm. Minimum distance between the two points having amplitude 2 mm is:

A
1 m

B
75 cm

C
60 cm

D
50 cm

Solution

λ = 2ℓ = 3m

Equation of standing wave y = 2A sin kx cos ωt y = A as amplitude is 2A.

A = 2A sin kx
Question 5
4 / -1

The average density of Earth’s crust 10 km beneath the surface is 2.7 gm/cm³. The speed of longitudnal seismic waves at that depth is 5.4 km/s. The bulk modulus of Earth’s crust considering its behavior as fluid at that depth, is :

A
7.9 × 10¹⁰ Pa

B
5.6 × 10¹⁰ Pa

C
7.9 × 10⁷ Pa

D
1.46 × 10⁷ Pa

Solution

= (5.40 x 10³ m/s)² (2.7 x 10³) = 7.9 x 10¹⁰ Pa.
Question 6
4 / -1

The second overtone of an open pipe A and a closed pipe B have the same frequencies at a given temperature. Both pipes contain air. The ratio of fundamental frequency of A to the fundamental frequency of B is:

A
3: 5

B
5: 3

C
5: 6

D
6: 5

Solution
Question 7
4 / -1

A thin uniform rod is suspended in vertical plane as a physical pendulum about point A. The time period of oscillation is T₀. Not counting the point A, the number 'n' of other points of suspension on rod such that the time period of oscillation (in vertical plane) is again T₀. Then the value of n is : (Since the rod is thin, consider one point for each transverse cross section of rod)

A
0

B
1

C
2

D
3

Solution

When the point of suspension is at a distance x from centre of length of rod, the time period of oscillation is where I is length of the rod.

The time period of oscillation will be same (T₀) if the point of suspension is a distance x = λ/2 or x = λ/6 from centre of the rod. Thus there will be three additional points.
Question 8
4 / -1

Two radio station that are 250m apart emit radio waves of wavelength 100m. Point A is 400m from both station. Point B is 450m from both station. Point C is 400m from one station and 450 m from the other. The radio station emit radio waves in phase. Which of the following statement is true ?

A
There will constructive interference at A and B, and destructive interference at C.

B
`There will be destructive interference at A and B, and constructive interference at C.

C
There will be constructive interference at B and C, and destructive interference at A.

D
There will be destructive interference at A, B and C.

Solution

At points A and B, path difference between the waves coming from two radio stations is zero. Hence there will be constructive interference at A and B,

For point C, path difference between the waves is 50 metre i.e. λ/2 so destructive interference takes places at point C.
Question 9
4 / -1

A particle performs SHM with a time period T and amplitude 'a'. The magnitude of average velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is :

A
a/T

B
2a/T

C
3a/T

D
a/2T

Solution

The magnitude of displacement in the given time interval = a/2

Time taken by the particle to cover a distance a/2 starting from rest = T/6

Hence the magnitude of average velocity over given time interval is
Question 10
4 / -1

A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration √3 g m/s². The period of small oscillations of the pendulum about its equilibrium position is (g = π² m/s²) :

A
1.0 sec

B
√2 sec

C
1.53 sec

D
1.68 sec

Solution

With respect to the cart, equilibrium position of the pendulum is shown. If displaced by small angle θ from this position, then it will execute SHM about this equilibrium position, time period of which is given by :