The planet Mars has two moons, if one of them has a period \(7\, hours,\, 30\, minutes\) and an orbital radius of \(9.0 \times 10^{3}\, {km} .\) Find the mass of Mars. \(\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}\)

A rectangular loop of sides \(12 \mathrm{~cm}\) and \(5 \mathrm{~cm}\), with its sides parallel to the \(x\)-axis and \(y\)-axis respectively moves with a velocity of \(5 \mathrm{~cm} / \mathrm{s}\) in the positive \(\mathrm{x}\) axis direction, in a space containing a variable magnetic field in the positive \(z\) direction. The field has a gradient of \(10^{-3} \mathrm{~T} / \mathrm{cm}\) along the negative \(\mathrm{x}\) direction and it is decreasing with time at the rate of \(10^{-5} \mathrm{~T} / \mathrm{s}\). If the resistance of the loop is \(6 \mathrm{~m} \Omega\), the power dissipated by the loop as heat is _______ \(\times 10^{-9} \mathrm{~W}\).

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?

A bimetallic strip consists of metals \(A\) and \(B\). It is mounted rigidly as shown. The metal \(A\) has higher coefficient of expansion compared to that of metal \(B\). When the bimetallic strip is placed in a cold both, it will :

A bullet of mass \(0.1\, kg\) is fired on a wooden block to pierce through it, but it stops after moving a distance of \(50\, cm\) into it. If the velocity of bullet before hitting the wood is \(10\) \(m / s\) and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is \('x' N.\) The value of \('x'\) to the nearest integer is................. \(N\)

If \(\mathrm{n}\) is the number density and \(\mathrm{d}\) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by _______.

In the given figure \(R_1=10 \Omega, R_2=8 \Omega, R_3=4 \Omega\) and \(R_4=8 \Omega\). Battery is ideal with emf \(12 \mathrm{~V}\). Equivalent resistant of the circuit and current supplied by battery are _______ respectively.

Two charges, each equal to \(q\), are kept at \(x = -a\) and \(x = a\) on the \(x-\)axis. A particle of mass \(m\) and charge \(q_0=\frac{q}{2}\) is placed at the origin. If charge \(q_0\) is given a small displacement \((y < < a)\) along the \(y-\)axis, the net force acting on the particle is proportional to

Select the correct statement from the following

A mass of \(50\,g\) of water in a closed vessel, with surroundings at a constant temperature takes \(2\, minutes\) to cool from \(30\,^oC\) to \(25\,^oC\). A mass of \(100\,g\) of another liquid in an identical vessel with identical surroundings takes the same time to cool from \(30\,^oC\) to \(25\,^o C\). The specific heat of the liquid is .......... \(kcal/kg\) (The water equivalent of the vessel is \(30\,g\).)