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 \(R = 8.3\,J/K\,mole\) ]

In an electric circuit, a cell of certain emf provides a potential difference of \(1.25\, {V}\) across a load resistance of \(5\, \Omega .\) However, it provides a potential difference of \(1\, {V}\) across a load resistance of \(2\, \Omega\). The \(emf\) of the cell is given by \(\frac{x}{10} v\). Then the value of \(x\) is ..... .

A \(70\, kg\) man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force \(F\) to raise himself The center of gravity rises by \(0.5\, m\) before he leaps. After the leap the \(c.g.\) rises by another \(1\, m\). The maximum power delivered by the muscles is : (Take \(g\, = 10\, ms^{-2}\))

The force required to stretch a wire of crosssection \(1 cm ^{2}\) to double its length will be ........ \( \times 10^{7}\,N\) (Given Yong's modulus of the wire \(=2 \times 10^{11}\,N / m ^{2}\) )

A tuning fork vibrates with frequency \(256\, Hz\) and gives one beat per second with the third normal mode of vibration of an open pipe . What is the length of the pipe? ... \(cm\) (Speed of sound of air is \(340\, ms^{-1}\))

A bar magnet is demagnetized by inserting it inside a solenoid of length \(0.2\, m\), \(100\, turns\), and carrying a current of \(5.2\, A\). The coercivity of the bar magnet is.....\(A/m\)

A circular disc \(D_1\) of mass \(M\) and radius \(R\) has two identical discs \(D_2\) and \(D_3\) of the same mass \(M\) and radius \(R\) attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis \(OO\)’, passing through the centre of \(D_1\) as shown in the figure, will

Given below are two statements: \(Statement\) \((I)\) : The limiting force of static friction depends on the area of contact and independent of materials. \(Statement\) \((II)\) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below:

The linear mass density of a thin rod \(A B\) of length \(L\) varies from \(A\) to \(B\) as \(\lambda( x )=\lambda_{0}\left(1+\frac{ x }{ L }\right),\) where \(x\) is the distance from A. If \(M\) is the mass of the rod then its moment of inertia about an axis passing through \(A\) and perpendicular to the rod is\(......ML^{2}\)

Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

A steel wire with mass per unit length \(7.0 \times 10^{-3}\,kg\,m ^{-1}\) is under tension of \(70\,N\). The speed of transverse waves in the wire will be \(.........m/s\)