A total of \(48 \mathrm{~J}\) heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by \(2^{\circ} \mathrm{C}\). The work done by the gas is _______. (Given, \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\).)

The magnetic intensity at the centre of a long current carrying solenoid is found to be \(1.6 \times 10^3 Am ^{-1}\). If the number of turns is 8 per cm, then the current flowing through the solenoid is \(................\,A\)

Two billiard balls of mass \(0.05\,kg\) each moving in opposite directions with \(10\,ms ^{-1}\) collide and rebound with the same speed. If the time duration of contact is \(t=0.005\,s\), then \(\dots N\)is the force exerted on the ball due to each other.

Light from a point source in air falls on a convex curved surface of radius \(20 \mathrm{~cm}\) and refractive index \(1.5.\) If the source is located at \(100 \mathrm{~cm}\) from the convex surface, the image will be formed at _______ \(\mathrm{cm}\) from the object.

A hot body, obeying Newton's law of cooling is cooling down from its peak value \(80\,^oC\) to an ambient temperature of \(30\,^oC\) . It takes \(5\, minutes\) in cooling down from \(80\,^oC\) to \(40\,^oC\).  ........  \(\min.\) will it take to cool down from \(62\,^oC\) to \(32\,^oC\) ? (Given \(ln\, 2\, = 0.693, ln\, 5\, = 1.609\))

Given below are two statements : Statement \(I :\) Stopping potential in photoelectric effect does not depend on the power of the light source. Statement \(II :\) For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light. In the light of above statements, choose the most appropriate answer from the options given below. Options :

A particle of mass \(M\) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation \(F=F_{0}\left(1-\left(\frac{t-T}{T}\right)^{2}\right)\) Where \(F_{0}\) and \(T\) are constants. The force acts only for the time internal \(2 T\). The velocity \(v\) of the particle after time \(2 {T}\) is -

When a certain photosensitive surface is illuminated with monochromatic light of frequency \(v\) , the stopping potential for the photo current is \(-V_0/2.\) When the surface is illuminated by monochromatic light of frequency \(v/2,\) the stopping potential is \(-V_0.\) The threshold frequency for photoelectric emission is

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

The pair of physical quantities not having same dimensions is :

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) For a simple microscope, the angular size of the object equals the angular size of the image. Reason \(R\) : Magnification is achieved as the small object can be kept much closer to the eye than \(25\, cm\) and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below:

\(K_1\) and \(K_2\) be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength \(\lambda_1\) and \(\lambda_2\), respectively. If \(\lambda_1=2\lambda_2\) then the work function of material is given by:

A train moves towards a stationary observer with speed \(34\, m/s\). The train sounds a whistle and its frequency registered by the observer is \(f_1\). If the speed of the train is reduced to \(17\, m/s\), the frequency registered is \(f_2\). If speed of sound is \(340\, m/s\), then the ratio \(f_1/f_2\) is