Engineering Questions with Answers - Multiple Choice Questions

# Wave Motion – 1

1 - Question

A body of mass 5kg hangs from a spring and oscillates with a time period of 2π seconds. If the body is removed, the length of the spring will decrease by?
a) g/k meters
b) k/g meters
c) 2π meters
d) g meters

Explanation: Here
T=2π√(m/k)=2π or m/k=1
In equilibrium,
mg=kd
d=mg/k=1×g=g meters.

2 - Question

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be ___________
a) T/4
b) T
c) T/2
d) 2T

Explanation: T=2π√(m/k), k=F/x
When the spring is cut into four equal parts,
k‘=F/(x/4)=4(F/x)=4k
T‘=2π√(m/k‘)=2π√(m/4k)=T/2.

3 - Question

Time period of a simple pendulum is 2sec. If its length is increased by 4 times, then its period becomes ___________
a) 8 sec
b) 12 sec
c) 16 sec
d) 4 sec

Explanation: T‘/T=√(l‘/l)=√(4l/l)=2
T‘=2T=2×2=4sec.

4 - Question

If the length of a simple pendulum is increased by 2%, then the time period ___________
a) Increases by 1%
b) Decreases by 1%
c) Increases by 2%
d) Decreases by 2%

Explanation: T∝√l
Percentage increase in time period,
∆T/T×100=1/2×∆l/l×100
=1/2×2%=1%.

5 - Question

A second’s pendulum is mounted in a rocket. Its period of oscillation will decrease when rocket is ___________
a) Moving down with uniform acceleration
b) Moving around the earth in geostationary orbit
c) Moving up with uniform velocity
d) Moving up with uniform acceleration

Explanation: When at rest, T=2π√(l/g)
When the rocket moves up with uniform acceleration,
T‘=2π√(l/(g+a))
Clearly, T‘<T.

6 - Question

A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by T=2π√(l/g), where g is equal to ___________
a) g
b) g-a
c) g+a
d) √(g2+a2 )

Explanation: As g and a are acting along perpendicular directions, the effective value of acceleration due to gravity is
g‘=√(g2+a2).

7 - Question

In case of a forced vibration, the resonance peak becomes very sharp when the ___________
a) Damping force is small
b) Restoring force is small
c) Applied periodic force is small
d) Quality factor is small

Explanation: When the damping force is small, the resonance peak is high and narrow.

8 - Question

A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinωt. If the amplitude of the particle is maximum for ω=ω1 and the energy of the particle maximum for ω=ω2, then?
a) ω1≠ω0 and ω2=ω0
b) ω1=ω0 and ω2=ω0
c) ω1≠ω0 and ω2≠ω0
d) ω1≠ω0 and ω2≠ω0

Explanation: In a driven harmonic oscillator, the energy is maximum at ω2=ω0 and amplitude is maximum at frequency, ω1 is lesser than ω0 in the presence of a damping of force. Therefore, ω1≠ω0 and ω2=ω0.

9 - Question

Two simple pendulums of lengths 5m and 20m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed.
a) 2 oscillations
b) 1 oscillation
c) 5 oscillations
d) 3 oscillations

Explanation: T1/T2 =√(l1/l2)=√(5/20)=1/2
T1=2T2
When the longer pendulum completes 2 oscillations, the shorter pendulum completes one oscillation and both are again in same phase.

10 - Question

The composition of two simple harmonic motions of equal periods at the right angle to each other and with a phase difference of π results in the displacement of the particle along?
a) Circle
b) Figure of eight
c) Straight line
d) Ellipse