A \(90 \mathrm{~kg}\) body placed at \(2 \mathrm{R}\) distance from surface of earth experiences gravitational pull of _______. ( \(\mathrm{R}=\) Radius of earth, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

10 kg of ice at \(-10^{\circ}C\) is added to 100 kg of water to lower its temperature from \(25^{\circ}C.\) Consider no heat exchange to surroundings. The decrement to the temperature of water is ___________ \(^{\circ}C.\)
(specific heat of ice \(= 2100\ J/Kg.^{\circ}C\), specific heat of water \(= 4200\ J/Kg.^{\circ}C\), latent heat of fusion of ice \(= 3.36 \times 10^{5}\ J/Kg\))

A proton, a deuteron and an \(\alpha\) particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speed is.................. in the ratio.

Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' \(\alpha\) '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

Angular momentum of a single particle moving with constant speed along circular path:

A hemispherical glass body of radius \(10\, cm\) and refractive index \(1.5\) is silvered on its curved surface. A small air bubble is \(6\, cm\) below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen 

Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.

A transparent cube of side \(d\), made of a material of refractive index \(\mu_2\), is immersed in a liquid of refractive index \(\mu_1(\mu_1 < \mu_2)\). A ray is incident on the face \(AB\) at an angle \(\theta \) (shown in the figure). Total internal reflection takes place at point \(E\) on the face \(BC\). The \(\theta\) must satisfy

If velocity \([V],\) time \([T]\) and force \([F]\) are chosen as the base quantities, the dimensions of the mass will be

A ball is spun with angular acceleration \(\alpha=6 t ^{2}-2 t\) where \(t\) is in second and \(\alpha\) is in \(rads\) \(^{-2}\). At \(t=0\), the ball has angular velocity of \(10\,rads\) \(^{-1}\) and angular position of \(4\,rad\). The most appropriate expression for the angular position of the ball is

A cylinder of radius \(R\) is surrounded by a cylindrical shell of inner radius \(R\) and outer radius \(2R\). The thermal conductivity of the material of the inner cylinder is \(K_1\) and that of the outer cylinder is \(K_2\). Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

A proton of mass ' \(m_{\mathrm{p}}\) ' has same energy as that of a photon of wavelength ' \(\lambda\) '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is _______.

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).