A solid sphere of mass \(1\,kg\) rolls without slipping on a plane surface. Its kinetic energy is \(7 \times 10^{-3}\,J\). The speed of the centre of mass of the sphere is \(.........cm s ^{-1}\).

A stationary particle breaks into two parts of masses \(m_A\) and \(m_B\) which move with velocities \(v_A\) and \(V_B\) respectively. The ratio of their kinetic energies \(\left(\mathrm{K}_B: \mathrm{K}_{\mathrm{A}}\right)\) is _______.

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength \(491\, nm\) is \(0.710\, V\). When the incident wavelength is changed to a new value, the stopping potential is \(1.43\, V\). The new wavelength is ....... \(nm.\)

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle \((\theta)\) of thread deflection in the extreme position will be :

Using equipartition of energy, the specific heat (in \(J\, kg^{-1}\, K^{-1}\) ) of aluminium at room temperature can be estimated to be ( atomic weight of aluminium \(= 27\))

In a microscope the objective is having focal length \(f_0=2 cm\) and eye-piece is having focal length \(f_{ e }=4 cm\). The tube length is 32 cm . The magnification produced by this microscope for normal adjustment is _________ .

Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below 

The bob of a pendulum was released from a horizontal position. The length of the pendulum is \(10 \mathrm{~m}\). If it dissipates \(10 \%\) of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : _______. [Use, \(\mathrm{g}: 10 \mathrm{~ms}^{-2}\) ]

At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as \(R\).)

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' \(h\) ' in terms of the angle of incidence ' \(i\) ' and angle of refraction ' \(r\) ', if the glass slab is placed in air medium?

The equivalent capacitance of the combination shown is

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is \(50 \,\%\) of its translational kinetic energy. The body is :