List of top Physics Questions

A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$ . If the initial number of both nuclei are the same, what is the ratio of the number of nuclei of $n_2$ to the number of nuclei of $n_1$ , after one half-life of $n_1$ ?

A spherical surface of radius of curvature $R$ , separates air from glass (refractive index = 1.5). The center of curvature is in the glass medium. A point object $O$ placed in air on the optic axis of the surface, so that its real image is formed at $I$ inside glass. The line $OI$ intersects the spherical surface at $P$ and $PO = PI$ . The distance $PO$ equals:

Consider a circular disc of radius 20 cm with center located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of the center of mass of the residual or remaining disc from the origin will be:

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness $h$ in terms of the angle of incidence $i$ and angle of refraction $r$ , if the glass slab is placed in air medium?

In the given circuit the sliding contact is pulled outwards such that the electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 Ω, the value of the current in the circuit will be A.

The position of a particle moving on x-axis is given by $x(t) = A \sin t + B \cos^2 t + Ct^2 + D$ , where $t$ is time. The dimension of $\frac{ABC}{D}$ is:

Three conductors of same length having thermal conductivity $k_1$ , $k_2$ , and $k_3$ are connected as shown in figure. Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of θ is ________ °C. (Given: $k_1$ = 60 Js⁻¹m⁻¹K⁻¹, $k_2$ = 120 Js⁻¹m⁻¹K⁻¹, $k_3$ = 135 Js⁻¹m⁻¹K⁻¹)

A light hollow cube of side length 10 cm and mass 10g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2}$ s, where the value of $y$ is:
(Acceleration due to gravity,

g = 10 \, \text{m/s}^2

, density of water =

10^3 \, \text{kg/m}^3

)

A particle is projected at an angle of $30^\circ$ from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is $h_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$ . The ratio $\frac{h_0}{h_1}$ is __________. [Take $g = 10 \, \text{m/s}^2$ ]

Given a thin convex lens (refractive index $\mu_2$ ), kept in a liquid (refractive index $\mu_1, \mu_1<\mu_2$ ) having radii of curvature $|R_1|$ and $|R_2|$ . Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

Regarding self-inductance:

\text{A}

: The self-inductance of the coil depends on its geometry.

\text{B}

: Self-inductance does not depend on the permeability of the medium.

\text{C}

: Self-induced e.m.f. opposes any change in the current in a circuit.

\text{D}

: Self-inductance is the electromagnetic analogue of mass in mechanics.

\text{E}

: Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

Identify the valid statements relevant to the given circuit at the instant when the key is closed.

$\text{A}$ : There will be no current through resistor R.
$\text{B}$ : There will be maximum current in the connecting wires.
$\text{C}$ : Potential difference between the capacitor plates A and B is minimum.
$\text{D}$ : Charge on the capacitor plates is minimum.
Choose the correct answer from the options given below:

The position vectors of two 1 kg particles, (A) and (B), are given by

\vec{r}_A = (\alpha_1 t \hat{i} + \alpha_2 t^2 \hat{j} + \alpha_3 t^3 \hat{k}) \, \text{m}

and

\vec{r}_B = (\beta_1 t \hat{i} + \beta_2 t^2 \hat{j} + \beta_3 t^3 \hat{k}) \, \text{m}, \text{ respectively; }

(\alpha_1 = 1 \, \text{m/s}, \, \alpha_2 = 3 \, \text{m/s}^2, \, \alpha_3 = 2 \, \text{m/s}^3, \, \beta_1 = 2 \, \text{m/s}, \, \beta_2 = -1 \, \text{m/s}^2, \, \beta_3 = 4 \, \text{m/s}^3),

where

t

is time, and

n

and

p

are constants. At

t = 1 \, \text{s}, \, |\vec{V}_A| = |\vec{V}_B|

and velocities

\vec{V}_A

and

\vec{V}_B

are orthogonal to each other. At

t = 1 \, \text{s}

, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is

\sqrt{L} \, \text{kgm}^2\text{s}^{-1}

. The value of

L

is ______.}

Given below are two statements:
Statement-I: The hot water flows faster than cold water.
Statement-II: Soap water has higher surface tension as compared to fresh water.
In the light of the above statements, choose the correct answer from the options given below:

A sub-atomic particle of mass $10^{-30}$ kg is moving with a velocity of $2.21 \times 10^6$ m/s. Under the matter wave consideration, the particle will behave closely like (h = $6.63 \times 10^{-34}$ J.s)

The electric flux is $\varphi = \alpha \sigma + \beta \lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively, and $\left( \frac{\alpha}{\beta} \right)$ represents

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is grams. Given Data: Latent heat of fusion of lead = $2.5 \times 10^4 \, \text{J kg}^{-1}$ and specific heat capacity of lead = 125 J kg $^{-1}$ K $^{-1}$ .

Match the List-I with List-II

Choose the correct answer from the options given below:

Refer to the circuit diagram given in the figure, which of the following observations are correct?

Observations:

A. Total resistance of circuit is 6 Ω

B. Current in Ammeter is 1 A

C. Potential across AB is 4 Volts

D. Potential across CD is 4 Volts

E. Total resistance of the circuit is 8 Ω

Choose the correct answer from the options given below:

A point particle of charge $Q$ is located at $P$ along the axis of an electric dipole 1 at a distance $r$ as shown in the figure. The point $P$ is also on the equatorial plane of a second electric dipole 2 at a distance $r$ . The dipoles are made of opposite charge $q$ separated by a distance $2a$ . For the charge particle at $P$ not to experience any net force, which of the following correctly describes the situation?

A solid sphere of mass $m$ and radius $r$ is allowed to roll without slipping from the highest point of an inclined plane of length $L$ and makes an angle of $30^\circ$ with the horizontal. The speed of the particle at the bottom of the plane is $v_1$ . If the angle of inclination is increased to $45^\circ$ while keeping $L$ constant, the new speed of the sphere at the bottom of the plane is $v_2$ . The ratio of $v_1^2 : v_2^2$ is:

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095 \, \text{J/m}^2$ and density $10^3 \, \text{kg/m}^3$ . The difference between pressure inside the bubble and atmospheric pressure is: Given

g = 10 \, \text{m/s}^2

.

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is $E_y = 9.3 \, \text{V/m}$ . Then, the magnetic field vector of the wave at that point is:

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected.

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$ . The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to: