If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :

A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\)  \((g\, = 10\, m\,s^{-2})\)

This question has statement \(1\) and statement \(2\) . Of the four choices given after the statements, choose the one that best describes the two statements. 
Statement \(- 1\): A point particle of mass m moving with speed \(u\) collides with stationary point particle of mass \(M\). If the maximum energy loss possible is given as \(f\) \(\left( {\frac{1}{2}m{v^2}} \right)\) then \( f = \left( {\frac{m}{{M + m}}} \right)\)  Statement \(-2\): Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A bottle has an opening of radius \(a\) and length \(b\). A cork of length band radius \(\left( {a + \Delta a} \right)\) where \(\left( {\Delta a <  < a} \right)\) is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is \(B\) and frictional coefficient between the bottle and cork is \(\mu \) then the force needed to push the cork into the bottle is

A person driving car at a constant speed of \(15\,m / s\) is approaching a vertical wall. The person notices a change of \(40\,Hz\) in the frequency of his car's horn upon reflection from the wall. The frequency of horn is ............ \(Hz\). (Given : Speed of sound : \(330\,m / s\) )

The disintegration rate of a certain radioactive sample at any instant is \(4250\) disintegrations per minute.\(10\) minutes later, the rate becomes \(2250\) disintegrations per minute. The approximate decay cons \(.........\min^{-1}\)

Assume that the displacement\((s)\) of air is proportional to the pressure difference \((\Delta p)\) created by a sound wave. Displacement\((s)\) further depends on the speed of sound \((v),\) density of air \((\rho)\) and the frequency \((f)\) If \(\Delta p \approx 10\, Pa , v  \approx 300\, m / s , p  \approx 1\, kg / m ^{3}\) and \(f \approx  1000 \,Hz\), then \(s\) will be the order of (take multiplicative constant to be \(1\) )

A circular disc reaches from top to bottom of an inclined plane of length \(l\). When it slips down the plane, if takes \(\mathrm{t} \mathrm{s}\). When it rolls down the plane then it takes \(\left(\frac{\alpha}{2}\right)^{1 / 2} \mathrm{t} s\), where \(\alpha\) is. _______.

In a hydrogen spectrum, \(\lambda\) be the wavelength of first transition line of Lyman series. The wavelength difference will be "a \(\lambda^{\prime}\) between the wavelength of \(3^{\text {rd }}\) transition line of Paschen series and that of \(2^{\text {nd }}\) transition line of Balmer Series where \(a=........\)

A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir raised by \(x\), its efficiency decreases to \(\frac{1}{6}\). The value of \(x\), if the temperature of hot reservoir is \(99^{\circ}\,C\), will be \(........\,K\)

A radioactive nucleus \(A\) with a half life \(T\), decays into a nucleus \(B.\) At \(t = 0\), there is no nucleus \(B\). At sometime \(t\), the ratio of the number of \(B\) to that of \(A\) is \(0.3\). Then, \(t\) is given by