In a meter bridge two gaps in the metallic strip are connected by \(3 \Omega\) and \(9 \Omega\) resistors. What should be the value of shunt that needs to be added to \(9 \Omega\) resistor to shift balancing point by \(25 \mathrm{~cm}\) ?

A particle is executing simple harmonic motion (S.H.M.). Its acceleration at a distance of $1 \mathrm{cm}$ from the mean position is $3 \mathrm{cm} {\mathrm{s}}^{-2}.$ If its velocity is $6 \mathrm{cm} {\mathrm{s}}^{-1}$ when it is at a distance of $2 \mathrm{cm}$ from its mean position, then the amplitude of S.H.M. is, 

Thermopile Bolometer is used to detect

If the heat required to increase the rms speed of 4 moles of a diatomic gas from \(v\) to \(\sqrt{3} \mathrm{v}\) is 83.1 kJ, then the initial temperature of the gas is (Universal gas constant \(=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) )

The ratio of the radii of two solid spheres of same mass is \(2: 3\). The ratio of the moments of inertia of the spitıres about their diameters is

A body thrown vertically upwards from the ground reaches a maximum height ' \(h\) '. The ratio of the kinetic and potential energies of the body at a height \(40 \%\) of \(h\) from the ground is

Two uniform stretched strings \(A\) and \(B\), made of steel, are vibrating under the same tension. If the first overtone of \(A\) is equal to the second overtone of \(B\) and if the radius of \(A\) is twice that of \(B\), the ratio of the lengths of the strings is

A reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by \(62^{\circ} \mathrm{C}\), the efficiency of the engine is doubled. The temperatures of the source and sink are

For a particle executing SHM, determine the ratio of average acceleration of the particle between extreme position and equilibrium position w.r.t. the maximum acceleration.

An electron in n-region of a p-n junction moves towards the junction with a speed of \(5 \times 10^5 \mathrm{~ms}^{-1}\). If the barrier potential of the junction is 0.45 V, then the speed with which the electron enters the p-region after penetration through the barrier is (Charge of the electron \(=1.6 \times 10^{-19} \mathrm{C}\) and mass of the electron \(=9 \times 10^{-31} \mathrm{~kg}\) )

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)

A moving body with a mass \(m_1\) and velocity \(u\) strikes a stationary body of mass \(m_2\). The masses \(m_1\) and \(m_2\) should be in the ratio \(\frac{m_1}{m_2}\), so as to decrease the velocity of the first body to \(\frac{2 u}{3}\) and giving a velocity of \(v\) to \(m_2\) assuming a perfectly elastic impact. Then, the ratio \(\frac{m_1}{m_2}\) is

A circular path of radius 75 m is banked at an angle of \(\tan ^{-1}(0.2)\). If the coefficient of static friction between the tyres of the car and the circular path is 0.1, then the maximum permissible speed of the car to avoid slipping is