A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed \(v\). The sphere and the cylinder reaches upto maximum heights \(h_1\) and \(h_2\), respectively, above the initial level. The ratio \(h_1: h_2\) is \(\frac{n}{10}\). The value of \(\mathrm{n}\) is __________.

The velocity-time graphs of a car and a scooter are shown in the figure. \((i)\) the difference between the distance travelled by the car and the scooter in \(15\, s\) and \((ii)\) the time at which the car will catch up with the scooter are, respectively

A circuit is arranged as shown in figure. The output voltage \({V}_{0}\) is equal to \(\ldots \ldots . {V}\).

A galvanometer has a resistance of \(50 \Omega\) and allows a maximum current of \(5 \mathrm{~mA}\) to pass. What is the necessary series resistance to connect to convert it to a voltmeter that can measure \(100 \mathrm{~V}\)?

A resistance is shown in the figure. Its value and tolerance are given respectively by

A positive ion \(A\) and a negative ion \(B\) has charges \(6.67 \times 10^{-19} \mathrm{C}\) and \(9.6 \times 10^{-10} \mathrm{C}\), and masses \(19.2 \times 10^{-27} \mathrm{~kg}\) and \(9 \times 10^{-27} \mathrm{~kg}\) respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is \(P \times 10^{45}\), where the value of 10\(P\) is _______.
(Take \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}\) and universal gravitational constant as \(6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\) )
Assume that charge may not be an integral multiple of electrons.

An object of mass \(m\) is suspended at the end of a massless wire of length \(L\) and area of cross\(-\)section, \(A\). Young modulus of the material of the wire is \(Y\). If the mass is pulled down slightly its frequency of oscillation along the vertical direction is

Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant)

Two wires of same length and thickness having specific resistances \(6\, \Omega \,cm\) and \(3 \,\Omega\, cm\) respectively are connected in parallel. The effective resistivity is \(\rho\, \Omega \,cm\). The value of \(\rho\) to the nearest integer, is ..... .

Two batteries with e.m.f \(12\ V\) and \(13\ V\) are connected in parallel across a load resistor of \(10\,\Omega\) . The internal resistances of the two batteries are \(1\,\Omega\) and \(2\,\Omega\) respectively. The voltage across the load lies between

A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90^{\circ}\), the ratio of instantaneous velocity to its average velocity is \(\pi: x \sqrt{2}\). The value of \(x\) will be \(.........\)

An experiment is performed to obtain the value of acceleration due to gravity \(g\) by using a simple pendulum of length \(L\). In this experiment time for \(100\, oscillations\) is measured by using a watch of \(1\, second\) least count and the value is \(90.0\, seconds\). The length \(L\) is measured by using a meter scale of least count \(1\, mm\) and the value is \(20.0\, cm\). The  error in the determination of \(g\) would be  ........... \(\%\)