A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

Suppose a uniformly charged wall provides a uniform electric field of \(2 \times 10^4 \mathrm{~N} / \mathrm{C}\) normally. A charged particle of mass \(2 \mathrm{~g}\) being suspended through a silk thread of length \(20 \mathrm{~cm}\) and remain stayed at a distance of \(10 \mathrm{~cm}\) from the wall. Then the charge on the particle will be \(\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}\) where \(\mathrm{x}=\) _______ [use \(g=10 \mathrm{~m} / \mathrm{s}^2\)]

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by \(E _{ x }= E _0 \sin ( kz -\omega t )\) \(B _{ y }= B _0 \sin ( kz -\omega t )\) Then the correct relation between \(E_0\) and \(B_0\) is given by

All electromagnetic wave is transporting energy in the negative \(z\) direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?

A block of mass \(m =1\, kg\) slides with velocity \(v=6\, m / s\) on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about \(O\) and swings as a result of the collision making angle \(\theta\) before momentarily coming to rest. If the rod has mass \(M =2 \,kg \) and length \(l=1\, m\) the value of \(\theta\) is approximately (Take \(\left.g=10 \,m / s ^{2}\right)\)

Three blocks \(A, B\) and \(C\) are lying on a smooth horizontal surface, as shown in the figure. \(A\) and \(B\) have equal masses, \(m\) while \(C\) has mass \(M\). Block \(A\) is given an initial speed \(v\) towards \(B\) due to which it collides with \(B\) perfectly inelastically. The combined mass collides with \(C\), also perfectly inelastically. The combined mass collides with \(C\), also perfectly inelastically if \(\frac{5}{6}^{th}\) of the initial kinetic energy is lost in whole process. What is value of \(M/m\) ?

In an experiment with a closed organ pipe, it is filled with water by \(\left(\frac{1}{5}\right)\) th of its volume. The frequency of the fundamental note will change by

The ratio for the speed of the electron in the \(3^{ rd }\) orbit of \(He ^{+}\)to the speed of the electron in the \(3^{\text {ad }}\) orbit of hydrogen atom will be

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of \(5 \times 10^{-4}\) is \(\dots \; kJ / m ^{3}\). Assume that material is elastic upto the linear strain of \(5 \times 10^{-4}\).

In an \(LCR\) series circuit, an inductor \(30 \,{mH}\) and a resistor \(1 \, \Omega\) are connected to an \(AC\) source of angular frequency \(300 \, {rad} / {s}\). The value of capacitance for which, the current leads the voltage by \(45^{\circ}\) is \(\frac{1}{x} \times 10^{-3} \, {F}\). Then the value of \(x\) is ..... .

Given below are two statement : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a rod lying freely is heated, no thermal stress is developed in it. Reason \(R :\) On heating the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below

A person travels \(x\) distance with velocity \(v_1\) and then \(x\) distance with velocity \(v_2\) in the same direction. The average velocity of the person is \(v\), then the relation between \(v , v _1\) and \(v _2\) will be :