Two projectiles are thrown with same initial velocity making an angle of \(45^{\circ}\) and \(30^{\circ}\) with the horizontal respectively. The ratio of their respective ranges will be.

If the velocity of a body related to displacement \({x}\) is given by \(v=\sqrt{5000+24 {x}} \;{m} / {s}\), then the acceleration of the body is \(\ldots \ldots {m} / {s}^{2}\)

A damped harmonic oscillator has a frequency of \(5\) oscillations per second. The amplitude drops to half its value for every \(10\) oscillations. The time it will take to drop to \(\frac{1}{1000}\) of the original amplitude is close to .... \(s\)

A small spherical ball of radius \(r\), falling through a viscous medium of negligible density has terminal velocity ' \(v\) '. Another ball of the same mass but of radius \(2 r\), falling through the same viscous medium will have terminal velocity _______.

The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\)

Two parallel long current carrying wire separated by a distance \(2 \mathrm{r}\) are shown in the figure. The ratio of magnetic field at \(\mathrm{A}\) to the magnetic field produced at \(C\) is \(\frac{x}{7}\). The value of \(x\) is _______.

A thin circular disc of mass \(M\) and radius \(R\) is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity \(\omega\). If another disc of same dimensions but of mass \(\mathrm{M} / 2\) is placed gently on the first disc co-axially, then the new angular velocity of the system is _______.

Which of the following phenomena can not be explained by wave theory of light ?

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is \(R_0= 10\, m\). What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity \(v = 20\, m/s\), on a horizontal surface ......... \(^o.\) \((g = 10\, m/s^2)\)

A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is _______.

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

A hydrogen atom makes a transition from \(n = 2\) to  \(n = 1\) and emits a photon. This photon strikes a doubly ionized lithium atom \((z = 3)\)  in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is

The electric current in a circular coil of \(2\) turns produces a magnetic induction \(B _{1}\) at its centre. The coil is unwound and is rewound into a circular coil of \(5\) turns and the same current produces a magnetic induction \(B _{2}\) at its centre.The ratio of \(\frac{ B _{2}}{ B _{1}}\) is.