A body is projected up with a velocity equal to \(\frac{3}{4}\) th of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth \(=R\) )

A wire of length \(50 \mathrm{~cm}\) and weighing \(10 \mathrm{gm}\) is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of \(50 \mathrm{~N} / \mathrm{m}\) and is stretched by \(1 \mathrm{~cm}\). If a wave pulse is produced on the string near the wall, then how much time will it take to reach the spring?

A circular hoop of radius $50 \mathrm{cm}$ and mass $1 \mathrm{kg}$ rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let $\text{'}v\text{'}$ be the velocity of the centre of the hoop when it ceases to slip. The ratio $v/{\omega }_0$ will be

A hollow spherical shell of radius \(r\) has a uniform charge density \(\sigma\). It is kept in a cube of edge \(3 r\) such that the centres of the cube and the shell coincide. Then the electric flux coming out of one face of a cube is ( \(\varepsilon_0\) - permittivity of free space)

A constant horizontal force \(\overrightarrow{\mathrm{F}}\) of magnitude \(10 \mathrm{~N}\) is applied to a block \(\mathrm{A}\) and this produces an acceleration of magnitude \(20 \mathrm{~m} / \mathrm{s}^2\). If this block \(A\) is then kept against another block B of mass \(1.5 \mathrm{~kg}\) as shown in figure and a force \(\mathrm{F}^{\prime}\) of \(20 \mathrm{~N}\) is applied, find the force on the block B. Neglect friction.

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)

The radiation emitted by a star \(A\) is 10000 times that of the sun. If the surface temperatures of the sun and the star \(A\) are \(6000 \mathrm{~K}\) and \(2000 \mathrm{~K}\) respectively, the ratio of the radii of the star \(A\) and the sun is :

A box of mass \(m\) is in equilibrium under the application of three forces as shown below. If the magnitude of \(\mathbf{F}_1\) is \(10 \mathrm{~N}\), what is the magnitude of \(\mathbf{F}_3\) ?

A uniform rod of length \(1.8 \mathrm{~m}\) suspended by an end is made to undergo small oscillations. Find the length of the simple pendulum having the mass and time period equal to that of the rod.

A source of frequency \(340 \mathrm{~Hz}\) is kept above a vertical cylindrical tube closed at lower end. The length of the tube is \(120 \mathrm{~cm}\). Water is slowly powred in just enough to produce resonance. Then, the minimum height (velocity of sownd \(=340 \mathrm{~m} / \mathrm{s}\) ) of the water level in the tube for that resonance is

A particle is exhibiting simple harmonic motion has its displacement \(x\) and velocity \(v\) related as \(4 v^2=25-x^2\). The time period of SHM is

A body moving with uniform acceleration, travels a distance of 25 m in the fourth second and 37 m in the sixth second. The distance covered by the body in the next two seconds is

When a sound wave of wavelength \(\lambda\) is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of wave is