The energy equivalent of \(1 \mathrm{~g}\) of substance is _______.

A \(15\,g\) mass of nitrogen gas is enclosed in a vessel at a temperature \(27\,^oC.\) Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about ...... \(kJ\) [Take \(R = 8.3\,J/K\,mole\) ]

A bullet of mass \(5\, g\), travelling with a speed of \(210\) \(m / s ,\) strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is \(0.030\, cal /\left( g -{ }^{\circ} C \right)\) \(\left(1\, cal =4.2 \times 10^{7}\, ergs \right)\) close to\(.......^oC\)

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field \((\vec{E} )\) and magnetic field \((\overrightarrow{ B })\) components.

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom ?

As shown in the figure a block of mass \(10\,kg\) lying on a horizontal surface is pulled by a force \(F\) acting at an angle \(30^{\circ}\), with horizontal. For \(\mu_{ s }=0.25\), the block will just start to move for the value of \(F..........\,N\) : \(\left[\right.\) Given \(\left.g =10\,ms ^{-2}\right]\)

Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of a to \(b\) is \(\frac{x}{2}\). The value of \(x\) is \(..............\)

The ratio of the equivalent resistance of the network (shown in figure) between the points \(a\) and \({b}\) when switch is open and switch is closed is \({x}: 8 .\) The value of \({x}\) is ..... .

A body of mass \(2 \mathrm{~kg}\) begins to move under the action of a time dependent force given by \(\overrightarrow{\mathrm{F}}=\left(6 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}\). The Power developed by the force at the time \(t\) is given by _______.

A solid sphere of radius \(r\) made of a soft material of bulk modulus \(K\) is surrounded by a liquid in a cylindrical container. A massless piston of area \(a\) floats on the surface of the liquid, covering entire crosssection of cylindrical container. When a mass \(m\) is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \(\left( {\frac{{dr}}{r}} \right)\) is 

The equation of a plane progressive wave is given by \(y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is _______ m/s.

A \(5 \,V\) battery is connected across the points \(X\) and \(Y\). Assume \(D_{1}\) and \(D_{2}\) to be normal silicon diodes. Find the current (in \(A\)) supplied by the battery if the \(+ve\) terminal of the battery is connected to point \(X\)