If momentum of a body is increased by \(20 \%\), then its kinetic energy increases by\(....\%\)

The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is  (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\)

Force between two point charges \(q_1\) and \(q_2\) placed in vacuum at ' \(r\) ' \(\mathrm{cm}\) apart is \(F\). Force between them when placed in a medium having dielectric \(\mathrm{K}=5\) at ' \(\mathrm{r} / 5\) ' \(\mathrm{cm}\) apart will be _______.

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below.

A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\).

A balloon was moving upwards with a uniform velocity of \(10\, {m} / {s}\). An object of finite mass is dropped from the balloon when it was at a height of \(75\, {m}\) from the ground level. The height of the balloon from the ground when object strikes the ground was around.(In \({m}\)) (Takes the value of \(g\) as \(10 \,{m} / {s}^{2}\) )

Sand is being dropped from a stationary dropper at a rate of \(0.5\,kgs ^{-1}\) on a conveyor belt moving with a velocity of \(5\,ms ^{-1}\). The 10.Power needed to keep belt moving with the same velocity will be.

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are :
\(\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2\) and \(\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}\). The free ends of rods A and B are maintained at \(400 \mathrm{~K}, 200 \mathrm{~K}\), respectively. The temperature of rods interface is ________ K, when equilibrium is established.

For the circuit shown below, calculate the value of \({I}_{{z}}\) : (In \({mA}\))

A \(20\,cm\) long metallic rod is rotated with \(210\,rpm\) about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field \(0.2\,T\) parallel to the axis exists everywhere. The emf developed between the centre and the ring is \(.......\,mV\).Take \(\pi=\frac{22}{7}\)

A galvanometer coil has \(500\) turns and each turn has an average area of \(3 \times 10^{-4}\, m ^{2}\). If a torque of \(1.5\,Nm\) is required to keep this coil parallel to magnetic field when a current of \(0.5\, A\) is flowing through it, the strength of the field (in \(T )\) is