\(5\,g\) and radius \(1\,cm\) is fixed to a thin stick \(AB\) of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about \(AB\) at \(25\) rotations per second in \(5\,s\) is close to

Two masses \(M _{1}\) and \(M _{2}\) are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass \(M _{2}\) is twice that of \(M_{1}\). the acceleration of the system is \(a_{1}\). When the mass \(M_{2}\) is thrice that of \(M_{1}\). The acceleration of The system is \(a_{2}\). The ratio \(\frac{a_{1}}{a_{2}}\) will be.

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness \(\left(t_{1}\right.\) and \(\left.t_{2}\right)\) as shown in figure. The two different dielectric material are separated by a conducting foil \(F\). The voltage of the conducting foil is \(.....V\)

This question has Statement \(-1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement \(1\) : Very large size telescopes are reflecting telescopes instead of refracting telescopes. Statement \(2\) : It is easier to provide mechanical support to large size mirrors than large size lenses.

'\(n\)' moles of an ideal gas undergoes a process \(A \rightarrow B\) as shown in the figure. The maximum temperature of the gas during the  process will be

In a Young's double slit experiment, slits are separated by \(0.5\ mm\), and the screen is placed \(150\ cm\) away. A beam of light consisting of two wavelengths, \(650\ nm\) and \(520\ nm\), is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is...... \(mm\)

A particle of mass \(2\, kg\) is on a smooth horizontal table and moves in a circular path of radius \(0.6\, m\). The height of the table from the ground is \(0.8\, m\). If the angular speed of the particle is \(12\, rad\, s^{-1}\), the magnitude of its angular momentum about a point on the ground right under the centre of the circle is ........ \(kg\, m^2\,s^{-1}\)

The bulk moduli of ethanol, mercury and water are given as \(0.9, 25\) and \(2 .2\) respectively in units of \(10^9\, Nm^{-2}\) . For a given value of pressure, the fractional compression in volume is \(\frac{{\Delta V}}{V}\). Which of the following statements about \(\frac{{\Delta V}}{V}\) for these three liquids is correct ?

A soap bubble of surface tension \(0.04 N / m\) is blown to a diameter of 7 cm . If \((15000- x ) \mu J\) of work is done in blowing it further to make its diameter 14 cm , then the value of x is _________ .\((\pi=22 / 7)\)

Suppose two planets (spherical in shape) of radii \({R}\) and \(2 {R}\), but mass \({M}\) and \(9\, {M}\) respectively have a centre to centre separation \(8\, {R}\) as shown in the figure. A satellite of mass \('{m}'\) is projected from the surface of the planet of mass \('M'\) directly towards the centre of the second planet. The minimum speed \('v'\) required for the satellite to reach the surface of the second planets is \(\sqrt{\frac{a}{7} \frac{G M}{R}}\) then the value of \('a'\) is \(....\) [Given: The two planets are fixed in their position]

A vessel contains \(16 \,g\) of hydrogen and \(128 \,g\) of oxygen at standard temperature and pressure. The volume of the vessel in \(cm ^{3}\) is

A prism of refractive index \(\mu\) and angle \(A\) is placed in the minimum deviation position. If the angle of minimum deviation is \(A,\) then the value of \(A\) in terms of \(\mu\) is

\(2\, moles\) of helium gas is mixed with \(3\, moles\) of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ....... \(J/mol\, K\) ? \((R = 8.3\, J/mol\, K)\)