Physics Test 290

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Physics Test 290

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Weekly Quiz Competition

Question 1
4 / -1

A ball is thrown vertically upwards with an initial velocity of 20 m/s from a height of 25 m. What is the total time taken by the ball to hit the ground? (Take g = 10 m/s²)

A
3 s

B
5 s

C
7 s

D
9 s

Solution

t = 5s
Question 2
4 / -1

A parallel-plate capacitor of plate area A and separation d is connected to a battery of constant voltage V. Initially it is filled with air. A dielectric slab of thickness d/2 and dielectric constant k is then fully inserted between the plates, leaving the other half d/2 as air. Which expression gives the new capacitance new C_new ?

A

B

C

D

Solution

Model as series layers: The capacitor becomes two capacitors in series: an air layer of thickness d/2 and a dielectric layer of thickness d/2.

The capacitance C of a parallel-plate capacitor with dielectric is:
Question 3
4 / -1

A solid sphere of radius R carries a uniform charge Q distributed throughout its volume. What is the potential difference between the center and the surface of the sphere, center surface V_center − V_surface , relative to infinity?

A

B

C

D

Solution
Question 4
4 / -1

A battery of emf E = 12 V and internal resistance r = 1Ω is connected to a network consisting of a 5Ω resistor in series with a parallel combination of 10Ω and 15Ω. What is the power dissipated in the 15Ω resistor?

A
2.4 W

B
3.6 W

C
4.0 W

D
1.6 W

Solution
Question 5
4 / -1

For a circular coil of radius R carrying current I, the magnetic field at a point on its axis at distance x from the center is proportional to:

A

B

C

D

Solution
Question 6
4 / -1

For a purely resistive AC circuit, the phase difference between the voltage and current is:

A
0°

B
90°

C
180°

D
45°

Solution
Question 7
4 / -1

Which of the following is a state variable in thermodynamics?

A
Heat

B
Work

C
Internal energy

D
None of these
Solution
A state variable (or state function) is a property of a thermodynamic system that depends only on its current equilibrium state, not on the path taken to reach that state. Examples include pressure (P), volume (V), temperature (T), and internal energy (U).

In contrast, a path function is a quantity whose value depends on the specific path taken between two states. Examples are heat (Q) and work (W).

Let's analyze the given options:
- Heat (Q): Heat is the energy transferred between systems due to a temperature difference. The amount of heat exchanged depends on the process (e.g., isothermal, adiabatic, isochoric). Therefore, heat is a path function.
- Work (W): Work is the energy transferred when a force acts over a distance. In thermodynamics, it often relates to the expansion or compression of a gas. The work done depends on the path on a P-V diagram. Therefore, work is a path function.
- Internal Energy (U): Internal energy represents the total energy contained within a system (microscopic kinetic and potential energies). The first law of thermodynamics, ΔU = Q − W, shows that while Q and W are path-dependent, their difference, ΔU, depends only on the initial and final states. Therefore, internal energy is a state variable.
Since internal energy is the only option that is a state variable, it is the correct answer.
Question 8
4 / -1

An alternating emf is given by E(t) = 220 sin ⁡(100πt)V and is applied across a pure resistor of resistance R = 110Ω. What is the average power (in watts) dissipated in the resistor ?

A
220

B
110

C
440

D
311

Solution
Question 9
4 / -1

A prism has refracting angle A = 60^∘ and refractive index μ = √3. A ray is incident on the first face at angle i = 60^∘.

What is the angle of deviation δ produced by the prism?

A
30^o

B
45^o

C
60^o

D
90^o

Solution
Question 10
4 / -1

What is the approximate radius of a uranium nucleus (A = 238)?

A
1.2 × 10⁻¹⁵m

B
7.4 × 10⁻¹⁵m

C
1.4 × 10⁻¹⁴m

D
2.9 × 10⁻¹⁴m

Solution