The gravitational field in a region is given by \(\overrightarrow g  = 5\,N/kg\hat i\, + \,12\,N/kg\hat j\). The change in the gravitational potential energy of a particle of mass \(1\, kg\) when it is taken from the origin to a point \((7\, m, - 3\, m)\) is .......  \(J\)

In \(5\, minutes,\) a body cools from \(75^{\circ} {C}\) to \(65^{\circ} {C}\) at room temperature of \(25^{\circ} {C}\). The temperature of body at the end of next \(5\, minutes\) is \(......\,{ }^{\circ} {C} .\)

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(S\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of 1 m from \(S\) and has a speed of \(1 m s ^{-1}\). The maximum value of \(\sigma\), if the electron strikes \(S\) at \(t=1 s\) is \(\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{ C }{ m ^2}\). The value of \(\alpha\) is __________ .

A steel wire having a radius of \(2.0\, mm\), carrying a load of \(4\, kg\), is hanging from a ceiling. Given that \(g = 3.1\pi \,m{s^{ - 2}}\) , what will be the tensile stress that would be developed in the wire?

A transverse wave travels on a taut steel wire with a velocity of \({v}\) when tension in it is \(2.06 \times 10^{4} \;\mathrm{N} .\) When the tension is changed to \(T\). the velocity changed to \(\frac v2\). The value of \(\mathrm{T}\) is close to

A particle of mass \(m\) moving with velocity \(v\) collides with a stationary particle of mass \(2m\). After collision, they stick together and continue to move together with velocity ........

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) An electric fan continues to rotate for some time after the current is switched off. Reason \(R:\) Fan continuous to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below.

As shown in figure, a \(70\,kg\) garden roller is pushed with a force of \(\overrightarrow{ F }=200\,N\) at an angle of \(30^{\circ}\) with horizontal. The normal reaction on the roller is \(.......\,N\) \(\left(\right.\) Given \(\left.g =10\,m s ^{-2}\right)\)

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?