A circular ring of mass \(10 \mathrm{~kg}\) rolls along a horizontal floor. The center of mass of the ring has a speed \(1.5 \mathrm{~m} / \mathrm{s}\). The work required to stop the ring is

Two spherical soap bubbles of radii \(r_1\) and \(r_2\) in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

The work to be done to produce a strain of \(10^{-3}\) in a steel wire of mass 2.96 kg and density \(7.4 \mathrm{~g} \mathrm{~cm}^{-3}\) is
(Young's modulus of steel \(=2 \times 10^{11} \mathrm{Nm}^{-2}\) )

A block of mass ' \(m\) ' with an initial kinetic energy ' \(E\) moves up an inclined plane of inclination ' \(\theta\) '. If ' \(\mu\) ' is the coefficient of friction between the plane and the body, the work done against friction before coming to rest is

A free neutron decays spontaneously into :

The efficiency of carnot engine is $\eta$ when its hot and cold reservoirs are maintained at temperature $T_1$ and $T_2$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $\left(\mathrm{\Delta }T\right)$ of the hot reservoir by keeping the cold one constant at $T_2$ is

A particle is projected from the ground with an initial speed of \(v\) at an angle of projection \(\theta\). The average velocity of the particle between its time of projection and time it reaches highest point of trajectory is

The energy \((E)\), angular momentum \((L)\) and universal gravitational constant \((G)\) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant \((h)\) is

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

A moving coil galvanometer has a rectangular wire coil of enclosed area \(0.001 \mathrm{~m}^2\) and 500 turns. The coil operates in a radial magnetic field of \(0.2 \mathrm{~T}\) and carries a current of \(6 \pi \times 10^{-8} \mathrm{~A}\). If the torsional spring constant is \(6 \times 10^{-7} \mathrm{~N}-\mathrm{m} / \mathrm{rad}\), then the angular deflection of the coil in radians is

Match Column A (layers in the ionosphere for skywave propagation) with Column B (their height range)

\(\begin{array}{llll}\mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D}\end{array}\)

If the first line of Lyman series has a wavelength \(1215.4 Å\), the first line of Balmer series is approximately

A radiation of energy \(E\) falls on a perfectly reflecting surface. The momentum transferred to the surface is (let \(c \equiv\) speed of light)