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A body of mass $m$ is taken from surface of earth to height of $5R$. If gravity at surface is $g_o$, then work done by external force to move the body is (neglect air resistance)

The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v [CPMT 1987]

A monochromatic light of wavelength λ is incident normally on a narrow slit of width 'a' to produce a diffraction pattern on the screen placed at a distance 'D' from the slit. With the help of relevant diagram, deduce the conditions for obtaining maxima and minima on the screen.

Rain pouring down at an angle $\alpha$ with the vertical has a speed of $10\text{m/s}$. A girl runs against the rain with the speed of $8\text{m/s}$ and sees that the rain makes an angle $\beta$ with the vertical, then relation between $\alpha$ and $\beta$ is

Which of the following graphs correctly represent adiabatic expansion?

A body of mass $1\text{kg}$ is subjected to a force of $20\text{N}$ for $10$ seconds after which the force ceases to act. What distance would it travel in the next $10$ seconds?

Figure shows a cylindrical tube with adiabatic wa lls and fitted with an adiabatic separator. The separator can be slid into the tube by an external mechanism. An ideal gas $(\gamma =1.5)$ is injected in the two slides at eual pressures and temperatures. The separator remains in equilibri um at the middle. It is now slid to a position where it divides the tube in the ratio 1 : 3. Find the ratio of the temperatures in the two parts of the vessel

Why do we have to do translation and then rotation during shifting of origin?

Obtain an expression for acceleration of the particle performing circular motion.

Find the charge appearing on each of the three capacitors shown in figure (31-E2).

Calculate the dipole moment of m-dicholorobenzene $[\mu =1.5D]$

Is the shape of the earth spheriod or geoid?

Two plane mirrors are inclined at an angle of ${30}^{\circ }$ with each other as shown in the figure. A light ray, incident on one of the mirror at an angle of incidence of ${60}^{\circ }$, after undergoing some reflections from the two mirror finally retraces its path and emerges out along the same line that is entered . The total number of times the ray is reflected before emerging out is

A particle is projected vertically upwards with a velocity of 20 m/sec. Find the time at which the distance travelled is twice the displacement

In an oscillating LC circuit, maximum charge on the capacitor is Q. The charge on this capacitor, when the energy is stored equally distributed between the electric and magnetic fields is

A plane e.m. wave of frequency 30 MHz travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is $E=6V{m}^{-1}$ along y-direction. Its magnetic field component B at this point would be

Figure shows a man of mass 55kg appear standing stationary with respect to a horizontal conveyor belt that is accelerating with $1m{s}^{-2}$. The net force acting on the man is

Gravitational field in a region is given by vector $(4\hat{i}+\hat{j})$. Work done by this field is zero when particle is moved along line.

The energy gap of silicon is about

When ${10}^{12}$ electrons are removed from a neutral metal sphere, the charge on the sphere becomes:

The string of a step rolling wheel is pulled by applying force F will different lines of action in two situations as shown. The wheel starts rolling without slipping due to application of the force :

A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency $\frac{9}{\pi }$ rps. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes ${37}^{\circ }$, the speed of the spot (a point) on the wall is

As shown in the figure, region BCDEF and ABFG are of refractive index 2.0 and 1.5 respectively. A particle O is kept at the mid of region BCEF. Final image of the object as seen by the eye is at a distance (curved part is a spherical one of radius 10 cm)

In a series ac circuit, the instantaneous voltage V(t) and current I(t) are given by $V\left(t\right)=5[cos\omega t+\sqrt{3}sin\omega t]$
$I\left(t\right)=5\left[sin\right(\omega t+\frac{\pi }{4}\left)\right],$ then

The displacement of the particle is given by $x=2t^3-6t$ in $\text{m}$. The acceleration of the particle at $2\text{sec}$ is

A satellite moves around the earth in a circular orbit of radius $r$ with speed $v$. If the mass of the satellite is $M$, its total energy is

Two cylindrical wires $A$ and $B$ are of the same material. Their lengths are in the ratio $1:2$ and the diameters are in the ratio $2:1$. If they are pulled by the same force, then increase in their respective lengths will be in the ratio

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with a constant angular acceleration $\alpha$. If the coefficient of static friction between the rod and bead is $\mu$, and gravity is neglected, then the time after which the bead starts slipping is:

A body of mass 400g slides on a rough horizontal surface. If the frictional force is 3.0 N, find (a) the angle made by the contact force on the body with the vertical and (b) the magnitude of the contact force. Take g = 10$\frac{m}{s^2}$

A body of mass $m$ rests on a horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between the body and surface will be

Two equal mass objects are moving in a circular path with constant speed as shown in figure. After how many collisions they will again meet at $A$.

In anomalous expansion of water, at what temperature the density water is maximum?

A uniform circular disc of radius $r$ is placed on a rough horizontal surface and given, a linear velocity $v_0$ and angular velcoity ${\omega }_0$ as shown. The disc comes to rest after moving some distance to right. It follows that

Why do we consider F=O for massless objects ?....Any other reason except , Acceleration = infinite

Stationary waves of frequency $300\text{Hz}$ are formed in a string, in which the velocity of wave is $200\text{m/s}$. The distance between a node and the consecutive antinode is

The graph of displacement v/s time is


Its corresponding velocity-time graph will be

A given object takes n times more time to slide down ${45}^{\circ }$ rough inclined plane as it takes to slide down a perfectly smooth ${45}^{\circ }$ incline. The coefficient of kinetic friction between the object and the incline is

A cubical block of mass m and edge a slides down a rough inclined plane of inclination $\theta$ with a uniform speed. Find the torque of the normal force acting on the block about its centre.