An object of mass \(0.5\, {kg}\) is executing simple harmonic motion. Its amplitude is \(5\, {cm}\) and time period (T) is \(0.2\, {s} .\) What will be the potential energy of the object at an instant \(t=\frac{T}{4}\) s starting from mean position. Assume that the initial phase of the oscillation is zero. (In \({J}\))

An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

A body of mass \(2\) kg begins to move under the influence of time dependent force \(\vec{F} = (2t\hat{i} + 6t^2\hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\)-axis respectively. The power produced by the force at \(t = 2\) s is _____ W.

The temperature \(\theta\) at the junction of two insulating sheets, having thermal resistances \(R _{1}\) and \(R _{2}\) as well as top and bottom temperatures \(\theta_{1}\) and \(\theta_{2}\) (as shown in figure) is given by

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election is \(v _{1}\). When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes \(v _{2}\). If \(v _{2}= x\) \(v _{1}\), the value of \(x\) will be...........

The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon \(= 7.36 \times 10^{22}\,kg,\) radius of the moon's orbit \(= 3 .8 \times 10^8\,m\) ).

A string \(A\) of length \(0.314\) m and Young's modulus \(2 \times 10^{10}\) N/m\(^2\) is connected to another string \(B\) of length and Young's modulus both twice of those of \(A\). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \(0.8\) kg. The net change in length of the combination is _____ mm. (radius of both the strings is \(0.2\) mm and acceleration due to gravity \(= 10\) m/s\(^2\)) (Mass of both strings is to be neglected as compared to the mass of load)

The \(I-V\) characteristics of an electronic device shown in the figure. The device is _______.

The ratio of intensities at two points \(P\) and \(Q\) on the screen in a Young's double slit experiment where phase difference between two wave of same amplitude are \(\pi / 3\) and \(\pi / 2\), respectively are

A gas balloon is going up with a constant velocity of \(10\) m/s. When this balloon reached a height of \(75\) m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take \(g=10\) m/s\(^2\))