Simple Harmonic Motion Test

Result

Simple Harmonic Motion Test - 15

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Question 1
1 / -0

A particle moves according to the law x = a cos πt/2. The distance covered by it in the time interval between t = 0 to t = 3 s is

A
2a

B
3a

C
4a

D
a

Solution

At time t = 0 particle is at x = a (at extreme position) and at t = 3s = 3T/4 it will be at mean position, x = 0

∴ distance covered will be 3a.
Question 2
1 / -0

A particle executing SHM has a maximum speed of 30 cm/s and a maximum, acceleration of 60cm/s⁻². The period of oscillation is

A
π sec

B
π/2 sec

C
2π sec

D
π/t sec

Solution

Man speed AW = 30cm/sec

Man acceleration = 60cm/sec−2

30 × W = 60

W = 2

2π/T = 2

T = π sec
Question 3
1 / -0

The x−t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4/3 s is

A
√3/32 π² cm/s²

B
–π²/32 cm/s²

C

D

Solution
Question 4
1 / -0

A tunnel has been dug through the centre of the earth and a ball is released in it. It executes S.H.M. with the time period:

A
42 minutes

B
1 day

C
1 hour

D
84.6 minutes

Solution

On falling deeper, the acceleration gets progressively smaller as it depends on distance from the center of the earth. Gravitational force at any point depends upon the mass inside the radius r.

Here, F is the force on the body and r is the distance from the centre. This is the equation of a body undergoing SHM with a time period of:

T = 5068s = 84.6 min
Question 5
1 / -0

Choose the correct statement regarding SHM,

A
Graphs of position,velocity and acceleration the functions with different phases

B
Graphs of position,velocity and acceleration start at different points of the y axis if drawn in the same xy plane

C
Position of body is a function of sine.

D
all the above

Solution

In an S.H.M→(1) graphs of position, velocity and acceleration with different phases (ii) Graphs of positions, velocity acceleration start at different points of y-axis if draw in same xy plane (iii)position of a body in a function of sine.
Question 6
1 / -0

The plot of velocity (v) versus displacement (x) of a particle executing simple harmonic motion is shown in figure. The time period of oscillation of particle is

A
π/2 s

B
π/s

C
2πs

D
3πs

Solution
Question 7
1 / -0

The displacement of a body executing SHM is given by x=Asin(2πt+π/3).The first time from t=0 when the velocity is maximum is

A
0.33sec

B
0.16sec

C
0.25sec

D
0.5sec

Solution

for other solutions, we will get higher values of time. but Since it is asking for the first time after t=0, the required solution will be t=0.33s
Question 8
1 / -0

Time period of a particle executing SHM is 88 sec. At t=0 it is at the mean position. The ratio of the distance covered by the particle in the 1st second to the 2n second is:

A

B

C

D

Solution
Question 9
1 / -0

Two particles execute SHM of the same amplitude and frequency along the same straight line. If they pass one another when going in opposite directions, each time their displacement is half their amplitude, the phase difference between them is

A
π/3

B
π/4

C
π/6

D
2π/3

Solution
Question 10
1 / -0

The time period of oscillation of a particle, that executes SHM, is 1.2s. The time, starting from mean position, at which its velocity will be half of its velocity at mean position is ?

A
0.1 s

B
0.2 s

C
0.4 s

D
0.6 s

Solution