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A point of mass is tied to one end of a cord whose other end is passes through a vertical hollow tube, caught in one hand. The point mass is being rotated in a horizontal circle of radius $2\text{m}$ with speed of $4\text{m/s}$. The cord is then pulled down so that the radius of the circle reduces to $1\text{m}$. Find the ratio of final kinetic energy and initial kinetic energy.

The height above the surface of Earth at which gravitational field intensity is reduced to $1\%$ of its value on the surface of Earth is ($R_e$ is radius of Earth)

The current and emf through an inductance differ in phase by:

A coil of $50$ turns is placed in a magnetic field of magnitude $B=0.25\text{Weber}$ as shown in figure. A current of $2\text{A}$ is flowing in the coil. The torque acting on the coil will be:

A disc rotates about its axis with a constant angular acceleration of$4\frac{rad}{s^2}.$Radial acceleration of a particle at a distance of$1cm$from the axis at the end of$1sec$is.

The image of an object placed on the principal axis of a concave mirror of focal length 12 cm is formed at a point which is 10 cm more distance from the mirror than the object. The magnification of the image is

In the state of weightlessness, a capillary tube is dipped in water, then water

A
molecule in a gas container hits a horizontal wall with speed 200 m
s^–1
and angle 30° with the normal,
and rebounds with the same speed. Is momentum conserved in the
collision? Is the collision elastic or inelastic?

Unit of electric flux is

Ship $A$ is travelling with a velocity of $5{\text{km h}}^{-1}$ due east. The second ship is heading ${30}^{\circ }$ east of north. What should be the speed of second ship if it is to always remain due north with respect to the first ship?

A molecule which cannot exist theoretically is :

In the circuit shown in the figure, the value of $V_0\left(t\right)$ (in volts) for $t\to \infty$ is .

1. 31.25

For the arrangement of the potentiometer shown in the figure, the balance point is obtained at a distance 75cm from A when the key k is open. The second balance point is obtained at 60 cm from A when the key k is closed. Find the internal resistance (in $\Omega$) of the battery $E_1$. ___

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Cutoff wavelength of X-rays coming from a Coolidge tube depends on the

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ respectively from the horizontal, then answer the following questions: If $v_1$ = $v_2$ and ${\theta }_1>{\theta }_2$, then choose the incorrect statement

Cutoff wavelength of X-rays coming from a Coolidge tube depends on the

A ball is thrown up with a certain velocity so that it reaches a height ${}^{\prime }{h}^{\prime }$. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

A particle is moving on x-axis has potential energy $U=x^2-4x+16$. If particle is released from $x=0$, locate the position where acceleration of the particle is zero.

The distance between the two charges +q and -q of a dipole is r. On the axial line at a distance d from the centre of dipole, the intensity is proportional to

In the electric field of a point charge q, a
certain point charge is carried from point A to B, C, D and E as shown in
figure. The work done is

A line passing through $(3,-2)$ and is parallel to the line $5x+6y+9=0$. The value of $x$ intercept made by the line is

A vessel contains $110\text{g}$ of water. The heat capacity of the vessel is equal to that of $10\text{g}$ of water. The initial temperature of water in the vessel is ${10}^{\circ }\text{C}$. While the water and vessel are in thermal equilibrium, $220\text{g}$ of hot water at ${70}^{\circ }\text{C}$ is poured into the vessel. Find the final temperature of the vessel + water system (neglecting radiation loss).

When light rays are incident on a prism at an angle of ${45}^{\circ }$, the minimum deviation is obtained. If the refractive index of the material of prism is $\sqrt{2}$ then the angle of the prism will be

Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated in the figure.

The output Y of the logic circuit given is

If an object made of substance A is rubbed with an object made of substance B, then A becomes positively charged and B becomes negatively charged. If, however, an object made of substance A is rubbed against an object made of substance C, then A become negatively charged. What will happen if an object made of substance B is rubbed against an object made of substance C?

Flint glass prism is joined by a crown glass prism to produce dispersion without deviation. The refractive indices of these prisms for yellow ray are $1.602$ and $1.500$ respectively. If the angle of flint glass prism is ${10}^{\circ }$. Then the angle of crown glass prism will be :

How did spaceship come from

A small copper ball of $5mm$ diameter at $500K$ is dropped into an oil bath whose temperature is $300K.$ The thermal conductivity of copper is $400W/mK,$ its density $9000kg/m^3$ and its specific heat $385J/kgK.$ If the heat transfer coefficient is $250W/m^{2}K$ and lumped analysis is assumed to be valid, the rate of fall of the temperature of the ball at the beginning of cooling will be , in $K/s,$

A box weighs $196\text{N}$ on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $g=10{\text{ms}}^{-2}$ at the North Pole and the radius of the earth $=6400\text{km})$