Physics Test 164

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Physics Test 164

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Question 1
4 / -1

The time taken by a particle performing SHM on a straight line to pass from point A to B where it's velocities are same is 2 seconds. After another 2 seconds it returns to B. The time period of oscillation is (in seconds):

A
2

B
4

C
6

D
8

Solution

From the given information it can be concluded that points A and B are equidistant from mean position.Hence from diagram it is clear that time period of oscillation is= 2 + 2 x 2 + 2 = 8 second.
Question 2
4 / -1

For a particle in S.H.M., if the amplitude of displacement is ‘a’ and the amplitude of velocity is ‘v’ the amplitude of acceleration is :

A
va

B

C

D
V/a

Solution
Question 3
4 / -1

A body performs SHM along the straight line segment ABCDE with C as the mid point of segment AE (A and E are the extreme position for the SHM). Its kinetic energies at B and D are each one fourth of its maximum value. If length of segment AE is 2R, then the distance between B and D is :

A

B
R/√2

C

D
√2 R

Solution

When the particle crosses D, its speed is half the maximum speed.
Question 4
4 / -1

A system is shown in the figure. The time period for small oscillations of the two blocks will be :

A

B

C

D
None

Solution
Question 5
4 / -1

Two light strings, each of length l, are fixed at points A and B on a fixed horizontal rod xy. A small bob is tied by both strings and in equilibrium, the strings are making angle 45° with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be :

A

B

C

D

Solution
Question 6
4 / -1

A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f₀ as shown in figure. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become:

A
f₀

B
√2f₀

C
2f₀

D
2√2f₀

Solution

where, ℓ is distance between point of suspension and centre of mass of the body. Thus, for the stick of length L and mass m :
Question 7
4 / -1

A 25 kg uniform solid sphere with a 20 cm radius is suspended by a vertical wire such that the point of suspension is vertically above the centre of the sphere. A torque of 0.10 N-m is required to rotate the sphere through an angle of 1.0 rad and then maintain the orientation. If the sphere is then released, its time period of the oscillation will be:

A
(π sec)

B
(4π sec)

C
(2π sec)

D
None of these

Solution

τ = -kθ

0.1 = -k(1.0), where k is torsional constant of the wire.

k = 1/10
Question 8
4 / -1

A rod of length l is in motion such that its ends A and B are moving along x-axis and y-axis respectively. It is given that rad/s always. P is a fixed point on the rod as shown in figure. Let M be the projection of P on x-axis. For the time interval in which q changes from 0 to π/2 ,

choose the correct statement :

A
The acceleration of M is always directed towards right

B
M executes SHM

C
M moves with constant speed

D
M moves with constant acceleration

Solution

Let BP = a ∴ x = OM = a sin θ = a sin (2t)

Hence M executes SHM with in the given time period and its acceleration is opposite to 'x' that means towards left
Question 9
4 / -1

Which of the following is greatest in SHM ? (assuming potential energy = 0 at mean position)

A
Average kinetic energy with respect to position

B
Average potential energy with respect to position

C
Average kinetic energy with respect to time

D
Average potential energy with respect to time

Solution
Question 10
4 / -1

m₁ & m₂ are connected with a light inextensible string with m₁ lying on smooth table and m₂ hanging as shown in figure. m₁ is also connected to a light spring which is initially unstretched and the system is released from rest :

A
system performs SHM with angular frequency given by

B
system performs SHM with angular frequency given by

C
tension in string will be zero when the system is released.

D
maximum displacement of m₁ will be

Solution

m₁moves towards right till the total kinetic energy acquired does not converted to potential energy.Hence (D) is also incorrect.Hence (B) is the answer