A disc is rolling without slipping on a surface. The radius of the disc is \(R\). At \(t=0\), the top most point on the disc is \(A\) as shown in figure. When the disc completes half of its rotation, the displacement of point \(A\) from its initial position is

A mass of \(50\,g\) of water in a closed vessel, with surroundings at a constant temperature takes \(2\, minutes\) to cool from \(30\,^oC\) to \(25\,^oC\). A mass of \(100\,g\) of another liquid in an identical vessel with identical surroundings takes the same time to cool from \(30\,^oC\) to \(25\,^o C\). The specific heat of the liquid is .......... \(kcal/kg\) (The water equivalent of the vessel is \(30\,g\).)

Two gases-argon (atomic radius \(0.07 \;\mathrm{nm}\),atomic weight \(40\) ) and xenon (atomic radius \(0.1\; \mathrm{nm},\) atomic weight \(140\) ) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to

Given below are two statements: Statement\(-I :\) An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement\(-II :\) Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below :

The electric field in an electromagnetic wave is given by \({E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})\) The energy contained in a cylinder of volume \({V}\) is \(5.5 \times 10^{-12} \, {J}\). The value of \({V}\) is \(......{cm}^{3}\) \(\left(\right.\) given \(\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)\)

If force \(\vec{F}=3 \hat{i}+4 \hat{j}-2 \hat{k}\) acts on a particle having position vector \(2 \hat{i}+\hat{j}+2 \hat{k}\) then, the torque about the origin will be

A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)

A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\frac{x}{y}\) is

When radiation of wavelength \(\lambda \) is incident on a metallic surface, the stopping potential is \(4.8\) volts. If the same surface is illuminated with radiation of double the wavelength, then the stopping potential becomes \(1.6\) volts. Then the threshold wavelength for the surface is

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of \(10\, mV\) is added to the base-emitter voltage, the base current changes by \(10 \mu A\) and the collector current changes by \(1.5 \,mA\). The load resistance is \(5 \,k \Omega\). The voltage gain of the transistor will be

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

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 .... \(ms^{-1}\)