If the time period of a two meter long simple pendulum is \(2\, s\), the acceleration due to gravity at the place where pendulum is executing \(S.H.M.\) is

A proton and a deutron ( \(\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})\) having same kinetic energies enter a region of uniform magnetic field \(\vec{B}\), moving perpendicular to \(\vec{B}\). The ratio of the radius \(r_d\) of deutron path to the radius \(r_p\) of the proton path is _______.

If two metallic plates of equal thicknesses and thermal conductivities \({K_1}\) and \({K_2}\) are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

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

List - \(I\)	List - \(II\)
\((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below :

The ratio of the density of oxygen nucleus \(\left({ }_8^{16} O \right)\) and helium nucleus \(\left({ }_2^4 He \right)\) is

The force required to stretch a wire of crosssection \(1 cm ^{2}\) to double its length will be ........ \( \times 10^{7}\,N\) (Given Yong's modulus of the wire \(=2 \times 10^{11}\,N / m ^{2}\) )

A particle is moving along the \(x-\)axis with its coordinate with the time '\(t\)' given be \(\mathrm{x}(\mathrm{t})=10+8 \mathrm{t}-3 \mathrm{t}^{2} .\) Another particle is moving the \(y-\)axis with its coordinate as a function of time given by \(\mathrm{y}(\mathrm{t})=5-8 \mathrm{t}^{3} .\) At \(\mathrm{t}=1\; \mathrm{s},\) the speed of the second particle as measured in the frame of the first particle is given as \(\sqrt{\mathrm{v}} .\) Then \(\mathrm{v}\) (in \(\mathrm{m} / \mathrm{s})\) is

\(A, B, C\) and \(D\) are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \(AD = C\, ln\, (BD)\) holds true. Then which of the combination is not a meaningful quantity ?

\(5\,g\) and radius \(1\,cm\) is fixed to a thin stick \(AB\) of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about \(AB\) at \(25\) rotations per second in \(5\,s\) is close to

A solenoid having area \(A\) and length ' \(l\) ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called: