\(27\) identical drops are charged at \(22\, V\,\,each.\) They combine to form a bigger drop. The potential of the bigger drop will be............ \(V.\)

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency \(512\,Hz\) produces first resonance when the tube is filled with water to a mark \(11\,cm\) below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency \(256\,Hz\) which produces first resonance when water reaches a mark \(27\,cm\) below the reference mark. The velocity of sound in air, obtained in the experiment, is close to .... \(ms^{-1}\)

A bullet looses \({\left( {\frac{1}{n}} \right)^{th}}\) of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be

A diatomic gas, having \(C_{p}=\frac{7}{2} R\) and \(C _{ v }=\frac{5}{2} R ,\) is heated at constant pressure. The ratio \(dU : dQ : dW :\)

A body of mass 2 kg moving with velocity of \(\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}\) enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \(\frac{5}{3}\) seconds, then velocity of the body when it emerges from force field is

A lens having refractive index 1.6 has focal length of 12 cm , when it is in air. Find the focal length of the lens when it is placed in water.
(Take refractive index of water as 1.28)

In an electrical circuit, a battery is connected to pass \(20\, C\) of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at \(15\, V\). The work done by the battery is ........... \(J\).

The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\).

A small soap bubble of radius \(4\,cm\)  is trapped inside another bubble of radius \(6\,cm\) without any contact. Let \(P_2\)  be the pressure inside the inner bubble and \(P_0\)  the pressure outside the outer bubble. Radius of another bubble with pressure difference \(P_2 - P_0\)  between its inside and outside would be....... \(cm\)

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

The ratio of the power of a light source \(S_1\) to that the light source \(S_2\) is \(2 . S_1\) is emitting \(2 \times 10^{15}\) photons per second at 600 nm . If the wavelength of the source \(S_2\) is 300 nm , then the number of photons per second emitted by \(S_2\) is _______ \(\times 10^{14}\).