Physics Test 65

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Physics Test 65

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Question 1
4 / -1

A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and centre of mass velocity V. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are ω_A and ω_B respectively. Then:

A
ω_A < ω_B

B
ω_A = ω_B

C
ω_A = ω

D
ω_B = ω

Solution

In the question, we are given two smooth spheres that are identical. The first sphere A moves with angular speed ω and centre of mass velocity v. The second sphere B is at rest and head-on, an elastic collision takes place there. As the given spheres are smooth, angular momentum will not be transferred between the spheres. Since this is a head on collision, sphere A transfers its velocity completely to sphere B. Further, sphere B begins to move whereas sphere A occupies the position of B and remains at rest. Hence the friction is zero, torque about their centre of mass is also having zero value. Thus the angular velocity doesn't change. Therefore, we can say that ω_A=ω,ω_B=0

Hence, the correct option is (C).
Question 2
4 / -1

The linear momentum, p of a body moving in one dimension varies with time, t according to the equation, p=a+bt², where, a and b are positive constants. The net force acting on the body is:

A
Constant

B
Proportional to t²

C
Inversely proportional to t

D
Proportional to t

Solution

Given,

p = a+bt²

Where, a and b are positive constants.

Differenciating with respect to t, we get

dp/dt = 2bt

∵ F = dp/dt

⇒F = 2bt

⇒F ∝ t

So, force is directly proportional to time.

Hence, the correct option is (D).
Question 3
4 / -1

Mass M is uniformly distributed only on thecurved surface of a thin hemispherical shell. A,B and C are three points inside the shell as shown in the diagram. Let the gravitational potential at points A,B and C be V_A,V_B and V_C, respectively. Then,

A
V_A > V_B > V_C

B
V_C > V_B > V_A

C
V_B > V_A > and V_B > V_C

D
V_A = V_B = V_C

Solution

Inside a hollow uniform shell, the gravitational field is zero. Due to the lower hemispherical shell, the direction of the field is in a downward direction at the given point. So, due to upper hemispherical shell gravitational field on A,B and C must be along the upward direction. So that, resultant field due to both hemispherical shells is zero. Potential always decreases in the direction of the field. So, the potential is decreasing along with A,B and C.

So, V_A>V_B>V_C

Hence, the correct option is (A).
Question 4
4 / -1

Two different gases at the same temperature have equal root mean square velocities (C_rms). If M is the molecular mass of the gas, then:

A

B
C_rms ∝ √M

C
C_rms ∝ M

D
C_rms = 0

Solution
Question 5
4 / -1

The refractive index of a material is given by the equation n = A+B / λ², where A and B are constant. The dimensional formula for B is:

A
[M⁰L² T^-1]

B
[M⁰L^-2 T⁰]

C
[M⁰L² T^-2]

D
[M⁰L² T⁰]

Solution
Question 6
4 / -1

A rod of length, l is given two velocities, v₁ and v₂ in opposite directions at its two ends at right angles to the length. The distance of the instantaneous axis of rotation from v₁ is:

A
0

B

C
v₁ / v₁-v₂ l

D
1/2

Solution
Question 7
4 / -1

The displacement time graph of a moving particle is shown below:

At which point, the instantaneous velocity of the particle is negative?

A
C

B
E

C
D

D
F

Solution

The slope of the tangent at any point on the displacement-time graph gives instantaneous velocity at that instant. In the given graph, the slope is negative at point E.

The velocity, (v)=ds/dt

Therefore, the instantaneous velocity at point E is negative.

Hence, the correct option is (B).
Question 8
4 / -1

A
740 J

B
750 J

C
730 J

D
745 J

Solution
Question 9
4 / -1

A hoop of mass M and radius R is hung from a support fixed in a wall. Its moment of inertia about the support is:

A
2MR²

B
3MR²

C
4MR²

D
6MR²

Solution

A hoop is a circular ring,

∴I₀= MR²

Where, M is a hoop of mass and R is radius.

By theorem of parallel axes,

I = I₀+ MR²

⇒ I = MR²+ MR²

⇒ I = 2MR²

Hence, the correct option is (A).
Question 10
4 / -1

The frequency f of vibration of mass m suspended from a spring of spring constant k is given by,

f = cm^xk^y

Where c is dimensionless constant. The values of x and y are respectively:

A
1/2, 1/2

B
- 1/2, 1/2

C
1/2, - 1/2

D
- 1/2, - 1/2

Solution