The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

In the given circuit the internal resistance of the \(18\,V\) cell is negligible. If \(R_1 = 400 \,\Omega ,\,R_3 = 100\,\Omega \) and \(R_4 = 500\,\Omega \) and the reading of an ideal voltmeter across \(R_4\) is \(5\,V,\) then the value of \(R_2\) will be ........... \(\Omega\)

A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF)

A square loop of side \(15 \mathrm{~cm}\) being moved towards right at a constant speed of \(2 \mathrm{~cm} / \mathrm{s}\) as shown in figure. The front edge enters the \(50 \mathrm{~cm}\) wide magnetic field at \(t=0\). The value of induced emf in the loop at \(t=10 \mathrm{~s}\) will be _______.

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of \(5\) times its mass? (Assume the collision to be head-on elastic collision)

Current passing through a wire as function of time is given as \(\mathrm{I}(\mathrm{t})=0.02 \mathrm{t}+0.01 \mathrm{~A}\). The charge that will flow through the wire from \(t=1 s\) to \(t=2 s\) is :

In the given circuit, \(C _1=2\,\mu F , C _2=0.2\,\mu F\), \(C _3=2\,\mu F , C _4=4\,\mu F,\) \(C _5=2\,\mu F , C _6=2\,\mu F\), the charge stored on capacitor \(C _4\) is \(.....\mu C\).

In a system two particles of masses \(m_1=3 \mathrm{~kg}\) and \(\mathrm{m}_2=2 \mathrm{~kg}\) are placed at certain distance from each other. The particle of mass \(m_1\) is moved towards the center of mass of the system through a distance \(2 \mathrm{~cm}\). In order to keep the center of mass of the system at the original position, the particle of mass \(\mathrm{m}_2\) should move towards the center of mass by the distance _______\(\mathrm{cm}\).

As shown in the figure, a current of \(2\,A\) flowing in an equilateral triangle of side \(4 \sqrt{3}\,cm\). The magnetic field at the centroid \(O\) of the triangle is: (Neglect the effect of earth's magnetic field.)

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and Rotational Equilibrium is :