A tuning fork of frequency \(480\, Hz\) is used in an experiment for measuring speed of sound \((\nu )\) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, \({\ell _1} = 30\,cm\) and \({\ell _2} = 70\,cm\). Then \(\nu\) is equal to ..... \(ms^{-1}\)

A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is

The fundamental frequency of vibration of a string stretched between two rigid support is \(50\,Hz\). The mass of the string is \(18\,g\) and its linear mass density is \(20\,g / m\). The speed of the transverse waves so produced in the string is \(..........\,ms ^{-1}\)

A machine gun of mass \(10\,kg\) fires \(20\,g\) bullets at the rate of \(180\) bullets per minute with a speed of \(100\,m s ^{-1}\) each. The recoil velocity of the gun is \(.............\,m/s\)

If a wave gets refracted into a denser medium, then which of the following is true?

A radar sends an electromagnetic signal of electric field \(\left( E _{0}\right)=2.25\,V / m\) and magnetic field \(\left( B _{0}\right)=1.5 \times 10^{-8}\,T\) which strikes a target on line of sight at a distance of \(3\,km\) in a medium After that, a pail of signal \((echo)\) reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time \(t_{0}\) from radar. then after how much time (in  \(\times 10^{-5}\,s\)) echo will reach to the radar?

Match List \(I\) with List \(II.\)

List \(I\)	List \(II\)
\((a)\) Rectifier	\((i)\) Used either for stepping up or stepping down the \(a.c.\) voltage
\((b)\) Stabilizer	\((ii)\) Used to convert \(a.c.\) voltage into \(d.c.\) voltage
\((c)\) Transformer	\((iii)\) Used to remove any ripple in the rectified output voltage
\((d)\) Filter	\((iv)\) Used for constant output voltage even when the input voltage or load current change

Choose the correct answer from the options given below:

When photons of wavelength \(\lambda _1\)  are incident on an isolated sphere, the corresponding stopping potential is found to be \(V.\)  When photons of wavelength \(\lambda _2\) are used, the corresponding stopping potential was thrice that of the above value . If light of wavelength \(\lambda _3\) is used then find the stopping potential for this case

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be \(......km\) (Take radius of earth \(=6400\,km\) and \(g =10\,ms^{-2}\) )

A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t=0\) the cylinder has a translational velocity \(v_0=49\) m/s, perpendicular to its axis and a rotational velocity \(v_0/4R\) about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction \(\mu_K=0.25\) and \(g=9.8\) m/s\(^2\))

The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2\). When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30°\) and phase difference is \(60°\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is _______ H.

Two coils of self inductance \(L _{1}\) and \(L _{2}\) are connected in series combination having mutual inductance of the coils as \(M\). The equivalent self inductance of the combination will be ...............

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant \(K\) is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \(\frac{3}{4} d\), where \('d'\) is the separation between the plates of parallel plate capacitor. The new capacitance \((C')\) in terms of original capacitance \(\left( C _{0}\right)\) is given by the following relation