Engineering Questions with Answers - Multiple Choice Questions

Home » MCQs » Engineering MCQs » Wave Motion – 1

# Wave Motion – 1

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

**
View Answer**

Answer: d

Explanation: Here

T=2π√(m/k)=2π or m/k=1

In equilibrium,

mg=kd

d=mg/k=1×g=g meters.

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

**
View Answer**

Answer: c

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.

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

**
View Answer**

Answer: d

Explanation: T‘/T=√(l‘/l)=√(4l/l)=2

T‘=2T=2×2=4sec.

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%

**
View Answer**

Answer: a

Explanation: T∝√l

Percentage increase in time period,

∆T/T×100=1/2×∆l/l×100

=1/2×2%=1%.

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

**
View Answer**

Answer: a

Explanation: When at rest, T=2π√(l/g)

When the rocket moves up with uniform acceleration,

T‘=2π√(l/(g+a))

Clearly, T‘<T.

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 )

**
View Answer**

Answer: d

Explanation: As g and a are acting along perpendicular directions, the effective value of acceleration due to gravity is

g‘=√(g2+a2).

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

**
View Answer**

Answer: a

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

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

**
View Answer**

Answer: a

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.

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

**
View Answer**

Answer: b

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.

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

**
View Answer**

Answer: c

Explanation: Let x = asinωt

y=bsin(ωt+π)=-bsinωt

x/a=y/b

y=-b/a×x

This is the equation of a straight line.