A projectile is thrown into air with velocity \(15 \mathrm{~m} / \mathrm{s}\) at an angle \(30^{\circ}\) with the horizontal. After what time its direction of motion is perpendicular to its initial direction? (Assume, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )

The nuclear forces are

The energy \((E)\), angular momentum \((L)\) and universal gravitational constant \((G)\) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant \((h)\) is

Consider a gas with molar mass $M.$ If the sound at frequency $f$ is introduced to a tube of this gas at temperature $T$ then an internal acoustic standing wave is set up with nodes separated by $L.$ The adiabatic constant $\left(\gamma =\frac{C_p}{C_v}\right)$ is

If the difference in the frequencies of the first and second lines of Lyman series of hydrogen atom is \(f\), then the difference in frequencies of the first and second lines of Balmer series of hydrogen atom is

Block $A$ of mass $3 \mathrm{kg}$ rests on another block $B$ of mass $7 \mathrm{kg}.$ The coefficient of friction between $A$ and $B$ is $0.4$ while the coefficient of friction between $B$ and the horizontal floor on which $B$ rests is $0.55.$ Find the force of friction between $A$ and $B,$ when a horizontal force of $50 \mathrm{N}$ is applied on the block $B.$
(Use $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$)

Two small spheres each having equal positive charge \(Q\) (Coulomb) on each are suspended by two insulating strings of equal length \(L\) (metre) from a rigid hook (shown in figure). The whole set up is taken into satellite where there is no gravity. The two balls are now held by electrostatic forces in horizontal position, the tension in each string is then

A block of mass \(m\) placed on a rough horizontal plane is pulled by a constant power \(P\). The coefficient of friction between the block and the surface is \(\mu\). The maximum velocity of the block will be

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

A quantity of monoatomic gas undergoes a process in which pressure is changed linearly with volume. The pressure and volume are changed from initial value \(\left(\mathrm{P}_{\mathrm{o}}, \mathrm{V}_{\mathrm{o}}\right)\) to final value \(\left(3 \mathrm{P}_{\mathrm{o}}, 3 \mathrm{~V}_{\mathrm{o}}\right)\). The heat absorbed by the gas during process is

Consider a vessel filled with a liquid upto height $H.$ The bottom of the vessel lies in the $X-Y$ plane passing through the origin. The density of the liquid varies with $Z$-axis as $\rho \left(z\right)={\rho }_0\left[2-{\left(\frac{z}{H}\right)}^2\right]$. If $P_1$ and $P_2$ are the pressures at the bottom surface and top surface of the liquid, the magnitude of $\left(P_1-P_2\right)$ is :

A system of two particles is having masses \(m_1\) and \(m_2\). If the particle of mass \(m_1\) is pushed towards the centre of mass of particles through a distance \(d\), by what distance the particle of mass \(m_2\) should be moved, so as to keep the centre of mass of particles at the original position?

A ball is falling freely from a height. When it reaches \(10 \mathrm{~m}\) height from the ground its velocity is \(v_0\). It collides with the ground and loses \(50 \%\) of its energy and rises back to height of \(10 \mathrm{~m}\). Then the velocity \(v_0\) is