Physics Test 140

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Physics Test 140

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Weekly Quiz Competition

Question 1
4 / -1

A solid ball rolls down a parabolic path ABC from a height h as shown in figure. Portion AB of the path is rough while BC is smooth. How high will the ball climb in BC ?

A
H = 5/7h

B
H = 5/2h

C
H = 7/5h

D
H = 3/7h

Solution

At B , total kinetic energy = mgh

Here,

m = mass of ball

The ratio of rotational to kinetic energy would be , Kr/Kt = 2/5

where, Kr = 2/7mgh and Kt = 5/7 mgh

In portion BC, friction is absent . Therefore, rotational K.E will remain constant and Translational K.E will convert into potential energy.

Hence, if H be the height to which ball climbs in BC, then

mgH = Kt

mgH = 5/7mgh

H = 5/7h
Question 2
4 / -1

A heat engine has an efficiency η. Temperatures of source and sink are each decreased by 100 K. Then, the efficiency of the engine.

A
Increases

B
Decreases

C
Remains constant

D
Becomes 1

Solution

where T₁ and T₂ are the temperatures of a source and sink respectively.

When T₁ and T₂ both are decreased by 100 K each, (T₁ - T₂) stays constant. T₁ decreases.

∴ η increases.
Question 3
4 / -1

A particle is moving in a uniform circular motion on a horizontal surface. Particle position and velocity at time t = 0 are shown in the figure in the coordinate system. Which of the indicated variable on the vertical axis is incorrectly matched by the graph shown alongside for particle's motion-

A
y component of force keeping particle moving in a circle

B
x component of velocity

C
Angular velocity of the particle

D
x coordinate of the particle

Solution
Question 4
4 / -1

In Coolidge tube experiment, if applied voltage is increased to three times, the short wavelength limit of continuous X - ray spectrum shifts by 20 pm. What is the initial voltage applied to the tube ?

A
20 kV

B
41 kV

C
52 kV

D
102 kV

Solution

Cut-off wavelength for continuous x-ray is given as :

∴ hc eV₀ = λ & hc 3 eV₀ = λ - Δλ

⇒ V₀ = 2 hc 3 e Δ λ = 41 kV
Question 5
4 / -1

A washer is made of metal having resistivity 10^–7 Ωm. The washer has inner radius 1 cm, outer radius 3 cm and thickness 1 mm. A magnetic field, oriented normal to the plane of the washer, has the time dependent magnitude B = (2t) tesla/sec. Find the current (in ampere) around the washer

A
2 amp

B
4 amp

C
6 amp

D
8 amp

Solution

Electric field at a general radial distance is E

E = rN/c

J = σE

Current in circular element di = j(dr)t
Question 6
4 / -1

Ends of two wires A and B having resistivity of same cross section area joined in series together to from a single wire. If the resistance of the joined wire does not change with temperature, then find the ratio of their lengths given that temperature coefficient of resistivity of wire A and B is

α_A= 4 ×10^–5/ °C and α_B = –6 × 10^–6/°C. Assume that mechanical dimensions do not change with temperature

A
3/7

B
10/3

C
3/10

D
1/2

Solution
Question 7
4 / -1

A cone of radius = height = r is under a liquid of density d. Its base is parallel to the free surface of the liquid at a depth H from it as shown in the figure. What is the net force due to liquid on its curved surface? (neglect atmospheric pressure)

A

B

C

D

Solution

Force due to liquid on curved surface = F

F = weight of liquid above the cone
Question 8
4 / -1

A spherical black body has a radius R and steady surface temperature T, heat sources ensure the heat evolution at a constant rate and distributed uniformly over its volume. What would be the new steady surface temperature of the object if the radius is decreased by half? Assume surrounding to be at absolute zero and heat evolution rate through unit volume remain same.

A
∜2 T

B

C
√2 T

D

Solution

Net heat getting generated in complete volume of sphere = rate of heat radiated by its surface
Question 9
4 / -1

The smallest length scale known in physics is the Planck length. It is an important ingredient in some current cosmological theories. Which of the following expressions could represent this Planck length? (Symbols has usual meaning)

A

B

C

D

Solution

Dimensional formula of only option D matches with length.
Question 10
4 / -1

In the figure shown two motors P₁ & P₂ fixed on a plank which is hanging with light string passing over fixed Pulley P. If the motors start winding the thread with angular velocity ω1 & ω2 then velocity of plank V is (here R₁ & R₂ are the radii of motor rotor respectively) [Given: ω1 = 2 rad/s, R₁ = 2m, ω2 = 2 rad/s, R₂ = 3m]

A
20 m/s

B
10m/s

C
5 m/s

D
4 m/s

Solution