A man (mass \(= 50\, kg\)) and his son (mass \(= 20\, kg\)) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of \(0.70\, ms^{-1}\) with respect to the man. The speed of the man with respect to the surface is ........ \(ms^{-1}\)

A thin \(1 \,m\) long rod has a radius of \(5\, mm\). A force of \(50\,\pi kN\) is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is \(0.01\, mm\), which of the following statements is false ?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R).
Assertion (A) : Magnetic monopoles do not exist.
Reason (R) : Magnetic field lines are continuous and form closed loops.
In the light of the above statements, choose the most appropriate answer from the options given below :

A rod of mass \(M\) and length \(L\) is lying on a horizontal frictionless surface. A particle of mass ' \(m\) ' travelling along the surface hits at one end of the rod with velocity \('u'\) in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses \(\left(\frac{m}{M}\right)\) is \(\frac{1}{x}\). The value of ' \(x\) ' will be ..... .

A signal of \(0.1\, kW\) is transmitted in a cable. The attenuation of cable is \(-5 \,dB\) per \(km\) and cable length is \(20\, km\). The power received at receiver is \(10^{-x} \, W\). The value of \(x\) is ....... . \(\left[\right.\) Gain in \(\left. dB =10 \log _{10}\left(\frac{ P _{0}}{ P _{i}}\right)\right]\)

If \(X\) and \(Y\) are the inputs, the given circuit works as _______.

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is _______.

A block of metal weighing \(2 \,kg\) is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of \(1 \,kgs ^{-1}\) and at a speed of \(10 \,ms ^{-1}\). Then, the initial acceleration of the block, in \(ms ^{-2}\), will be .................

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

A mirror is used to produce an image with magnification of \(\frac{1}{4}\). If the distance between object and its image is 40 cm , then the focal length of the mirror is ________

Unpolarized light of intensity \(I_0\) incident on surface of a block of glass at Brewster's angle. In that case, which one of ihe following statements is true ?

The electric fields of two plane electromagnetic plane waves in vacuum are given by \(\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx})\) and \(\overrightarrow{\mathrm{E}}_{2}=\mathrm{E}_{0} \hat{\mathrm{k}} \cos (\omega \mathrm{t}-\mathrm{ky})\) At \(t=0,\) a particle of charge \(q\) is at origin with a velocity \(\overrightarrow{\mathrm{v}}=0.8 \mathrm{c} \hat{\mathrm{j}}\) (\(c\) is the speed of light in vacuum). The instantaneous force experienced by the particle is