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A body is executing simple harmonic motion with frequency '$n$', the frequency of its potential energy is
The average thermal energy for a mono-atomic gas is : ($k_B$ is Boltzmann constant and T, absolute temperature)
A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm will be
In a certain region of space with volume $0.2 \text{ m}^3$, the electric potential is found to be $5 \text{ V}$ throughout. The magnitude of electric field in this region is :
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is $0.25 \ \Omega$. What will be the effective resistance if they are connected in series?
From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' times 'MR^2'. Then the value of 'K' is
Three resistors having resistances $r_1$, $r_2$ and $r_3$ are connected as shown in the given circuit. The ratio $\frac{i_3}{i_1}$ of currents in terms of resistances used in the circuit is
Match Column - I and Column - II and choose the correct match from the given choices. Column - I: (A) Root mean square speed of gas molecules, (B) Pressure exerted by ideal gas, (C) Average kinetic energy of a molecule, (D) Total internal energy of 1 mole of a diatomic gas. Column - II: (P) $\frac{1}{3}nm\bar{v}^2$, (Q) $\sqrt{\frac{3RT}{M}}$, (R) $\frac{5}{2}RT$, (S) $\frac{3}{2}k_BT$.
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is
The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is
A parallel plate capacitor has a uniform electric field $\vec{E}$ in the space between the plates. If the distance between the plates is '$d$' and the area of each plate is '$A$', the energy stored in the capacitor is ($\varepsilon_0$ = permittivity of free space)
A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively
A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by
A uniform rod of length $200 \text{ cm}$ and mass $500 \text{ g}$ is balanced on a wedge placed at $40 \text{ cm}$ mark. A mass of $2 \text{ kg}$ is suspended from the rod at $20 \text{ cm}$ and another unknown mass '$m$' is suspended from the rod at $160 \text{ cm}$ mark as shown in the figure. Find the value of '$m$' such that the rod is in equilibrium. ($g = 10 \text{ m/s}^2$)
A car starts from rest and accelerates at $5\text{ m/s}^2$. At $t = 4\text{ s}$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6\text{ s}$? (Take $g = 10\text{ m/s}^2$)
A wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q
When two monochromatic lights of frequency, $Q$ and $\frac{Q}{2}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_s}{2}$ and $V_s$ respectively. The threshold frequency for this metal is
When light propagates through a material medium of relative permittivity $\epsilon_r$ and relative permeability $\mu_r$, the velocity of light, $v$ is given by (c-velocity of light in vacuum)
An electric dipole is placed at an angle of $30^\circ$ with an electric field of intensity $2 \times 10^5$ N C$^{-1}$. It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.
A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is