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The ratio of hydraulic stress to the corresponding strain is known as:

A body is dropped from rest at a height of 150m and similarly another body is dropped from the rest from a point 100m above the ground what is there difference in height after they have fallen in 2 sec and in 3 sec.

An electron of mass m and charge e is accelerated from rest through a potential difference v in vacuum. What speed will it acquire?

The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are gamma 1 and gamma 2 respectively. If the coefficient of linear expansion of vessel A is alpha, the coefficient of linear expansion of vessel B is?

27 identical drops of mercury are charged to the same potential of 10 V.what will be the potential if all the charged drops are made to combine to form one large drop ? Assume the drops to be spherical

A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant

In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron

You are given a rod of length 'L'. The linear mass density varies as ${\lambda }^{\prime }$. $\lambda =a+bx$. Here a & b are constants and the mass of the rod increases as x increases. Find the mass of the rod.

A test charge of 3nC is placed at origin and experiences a force of 9 x 10^-4 N. The electric field at origin is:

A swimmer crosses the river so as to reach the opposite point, along the line making an angle of ${45}^o$ with the direction of flow. Velocity of the river water is $5m/s$. Swimmer takes 12 seconds to cross the river of width $60m$. The velocity of the swimmer (in $m/s$) with respect to flowing water will be:

If a simple pendulum is taken to a place where g decreases by 2%, then the time period

The degree of freedom for monoatomic gas is:

A liquid cools down from ${70}^{\circ }C$ to ${60}^{\circ }C$ in 5 minutes. The time taken to cool it from ${60}^{\circ }C$ to ${50}^{\circ }C$ will be

Two resistances X and Y are in the left and right gaps of a meter bridge. The balance point is 40 cm from left.Two resistances of $10\Omega$ each are connected in series with X and Y separately. The balance point is 45 cm. The value of X and Y are

If the degree of freedom of a gas are f, then the ratio of two specific heats $\frac{C_p}{C_v}$ is given by

The rectangular wire-frame, shown in figure (38-E22), has a width d, mass m, resistance R and a large length. A uniform magnetic field B exists to the left of the frame. A constant force F starts pushing the frame into the magnetic field at t = 0. (a) Find the acceleration of the frame when its speed has increased to v. (b) Show that after some time the frame will move with a constant velocity till the whole frame enters into the magnetic field. Find this velocity $v_0$. (c) Show that the velocity at time t is given by

$v=v_0(1-e^{-Ft/m{v}_0})$

A magnetic flux of $8\times {10}^{-4}$ weber is linked with each turn of a 200 - tunr coil when there is an electric current of 4 A in it. Calculate the self - inductance of the coil.

A parallel plate capacitor $C$ with plates of unit area and separation $d$ is filled with a liquid of dielectric constant $K=2$. The level of liquid is $\frac{d}{3}$ initially. Suppose the liquid level decreases at a constant speed $V$, the time constant as a function of time $t$ is

Four particles having masses, m, 2m, 3m and 4m are placed at the four corners of a square of edge a. Find the gravitational force acting on a particle of mass m placed at the centre.

A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillations. If the block makes 5 oscillations each second, what is the mass of the block ?

The statement $A\to (B\to A)$ is equivalent to:

The velocity of light in a medium is half its velocity in air. If ray of light emerges from such a medium into air, the angle of incidence, at which it will be totally internally reflected, is

Find the values of the following questions:

$co{s}^{-1}\left(\frac{1}{2}\right)+2si{n}^{-1}\left(\frac{1}{2}\right)$

A cubical block of side '$a$' moving on horizontal frictionless surface with velocity '$v$' hits a small nail [coefficient of restitution is e = 0] and rotates about it. Angular velocity of block after hitting the nail is

A rod of mass m and length l is kept on a smooth wedge of mass M as shown in the figure. If the system is released, find the speed of the wedge when the rod hits the ground level, neglecting friction in all contacting surfaces.

A hollow sphere of radius r rolls without slipping in a hemisphere of radius 4r. Calculate the frequency of small oscillations, about point P as shown in figure.

A bobbin is pushed along on a rough stationary horizontal surface as shown in the figure. The board is kept horizontal and there is no slipping at any contact points. Find the distance moved by the board when distance moved by the axis of the bobbin is ℓ.

Particle of mass 0.3 kg is subjected to a force F = –kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin:

When one centimeter thick surface is illuminated with light of wavelength $\lambda$, the stopping potential is V. When the same surface is illuminated by light of wavelength 2$\lambda$, the stopping potential is $\frac{V}{3}$ . Threshold wavelength for metallic surface is :

The square of angular speed of the electron in the $n^{th}$ orbit of Bohr’s hydrogen atom is:

The focal length of a plano convex lens when curved surface is silvered and the object is in front of plane surface is

A man runs towards a mirror at a speed $+6\text{m/s}$. If the mirror is at rest, his image will have a velocity (with respect to man)

In the circuit shown in figure reading of voltmeter is $V_1$, when only $S_1$ is closed, reading of voltmeter is $V_2$, when only $S_2$ is closed. The reading of voltmeter is $V_3$, when both $S_1$ and $S_2$ are closed, then

A ball is rotating in circle of radius $r$ with constant speed $u\text{m/s}$ as shown in figure. When ball is at point $a$, find the magnitude of torque acting on ball about point $b$.

If $h_1$ and $h_2$ be the greatest heights in the two paths of projectile for a given range, then the range is given by:

Resistance of a wire at temperature $t^{\circ }C$ is
$R=R_0(1+at+b{t}^2)$
Here, $R_0$ is the temperature at $0^{\circ }C$. The temperature coefficient of resistance at temperature t is

The energy required to break a mercury drop of 1cm radius into 1000 small drops of equal size is….Joule (given the surface tension of mercury is $0.4N.m^{-1}$)

One mole of a diatomic gas undergoes a process $P=\frac{P_o}{1+(\frac{V}{V_o}{)}^3}$ where $P_o$ and $V_o$ are constants. The translational kinetic energy of the gas when $V=V_o$ is given by

A container is partially filled with a liquid of density ${\rho }_2$ in which a capillary tube of radius $r$ is vertically inserted. Now another liquid of density ${\rho }_1({\rho }_1<{\rho }_2)$ is slowly poured in the container to a height $h$ as shown. There is only denser liquid in the capillary tube. The rise of denser liquid in the capillary tube is also $h$. Assuming zero contact angle, the surface tension of liquid is