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A ball is thrown vertically downward with a velocity of $20 \text{ m/s}$ from the top of a tower. It hits the ground after some time with a velocity of $80 \text{ m/s}$. The height of the tower is : ($g = 10 \text{ m/s}^2$)
A body is executing simple harmonic motion with frequency '$n$', the frequency of its potential energy is
Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt{3}$.
A resistance wire connected in the left gap of a metre bridge balances a $10 \ \Omega$ resistance in the right gap at a point which divides the bridge wire in the ratio $3 : 2$. If the length of the resistance wire is $1.5 \text{ m}$, then the length of $1 \ \Omega$ of the resistance wire is :
The average thermal energy for a mono-atomic gas is : ($k_B$ is Boltzmann constant and T, absolute temperature)
A spherical conductor of radius $10 \text{ cm}$ has a charge of $3.2 \times 10^{-7} \text{ C}$ distributed uniformly. What is the magnitude of electric field at a point $15 \text{ cm}$ from the centre of the sphere? ($\frac{1}{4\pi \epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2$)
If E and G respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of
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 :
An inductor of inductance $L$, a capacitor of capacitance $C$ and a resistor of resistance $R$ are connected in series to an ac source of potential difference $V$ volts as shown in figure. Potential difference across $L$, $C$ and $R$ are 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through $LCR$ series circuit is $10\sqrt{2}$ A. The impedance of the circuit 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?
Column-I gives certain physical terms associated with flow of current through a metallic conductor. Column-II gives some mathematical relations involving electrical quantities. Match Column-I and Column-II with appropriate relations. Column-I: (A) Drift Velocity, (B) Electrical Resistivity, (C) Relaxation Period, (D) Current Density. Column-II: (P) $\frac{m}{ne^2\rho}$, (Q) $nev_d$, (R) $\frac{eE}{m}\tau$, (S) $\frac{E}{J}$
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
In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:
A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of
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 escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is
In the product $\vec{F} = q(\vec{v} \times \vec{B}) = q\vec{v} \times (B\hat{i} + B\hat{j} + B_0\hat{k})$. For $q = 1$ and $\vec{v} = 2\hat{i} + 4\hat{j} + 6\hat{k}$ and $\vec{F} = 4\hat{i} - 20\hat{j} + 12\hat{k}$. What will be the complete expression for $\vec{B}$?
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