Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same \((M)\) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end \(A\) of the handle will be ....... \(Mr^2\)?

A charge particle of \(2\,\mu\,C\) accelerated by a potential difference of \(100\,V\) enters a region of uniform magnetic field of magnitude \(4\,m\,T\) at right angle to the direction of field. The charge particle completes semicircle of radius \(3\,cm\) inside magnetic field. The mass of the charge particle is \(........\times 10^{-18}\,kg\).

A sample of gas at temperature \(\mathrm{T}\) is adiabatically expanded to double its volume. Adiabatic constant for the gas is \(\gamma=3 / 2\). The work done by the gas in the process is _______. \((\mu=1 \mathrm{~mole})\)

As shown in the figure, a particle of mass \(10\) \(kg\) is placed at a point \(A\). When the particle is slightly displaced to its right, it starts moving and reaches the point \(B\). The speed of the particle at \(B\) is \(x\, m / s\). (Take \(\left. g =10\, m / s ^{2}\right)\) The value of \('x'\) to the nearest integer is.........

Which of the following are true? \(A.\) Speed of light in vacuum is dependent on the direction of propagation. \(B.\) Speed of light in a medium in independent of the wavelength of light. \(C.\) The speed of light is independent of the motion of the source. \(D.\) The speed of light in a medium is independent of intensity. Choose the correct answer from the option given below :

A metallic sphere cools from \(50^{\circ} C\) to \(40^{\circ} C\) in \(300 \,s.\) If atmospheric temperature around is \(20^{\circ} C ,\) then the sphere's temperature after the next \(5\) minutes will be close to\(.....C\)

A heat source at \(T = 10^3\, K\) is connected to another heat reservoir at \(T = 10^2\, K\) by a copper slab which is \(1\, m\) thick. Given that the thermal conductivity of copper is \(0.1\, WK^{-1}\, m^{-1}\), the energy flux through it in the steady state is ........... \(Wm^{-2}\)

A monochromatic light is incident on a metallic plate having work function \(\phi\). An electron, emitted normally to the plate from a point \(A\) with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point \(B\). The distance between A and B is :
(Given : The magnitude of charge of an electron is e and mass is \(\mathrm{m}, \mathrm{h}\) is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

Given below are two statements: \(Statement\) \(I\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. \(Statement\) \(II\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below

Two metallic wires \(P\) and \(Q\) have same volume and are made up of same material. If their area of cross sections are in the ratio \(4: 1\) and force \(F_1\) is applied to \(\mathrm{P}\), an extension of \(\Delta l\) is produced. The force which is required to produce same extension in \(Q\) is \(\mathrm{F}_2\).The value of \(\frac{\mathrm{F}_1}{\mathrm{~F}_2}\) is _______.

A particle is subjected two simple harmonic motions as :
\(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is :