Two identical photo-cathodes receive light of frequencies $$f_1$$ and $$f_2$$. If the velocities of the photo electrons (of mass $$m$$ ) coming out are respectively $$v_1$$ and $$v_2,$$ then

A magnetic needle lying parallel to a magnetic field requires $$W$$ units of work to turn it through $$60^{\circ }.$$ The torque needed to maintain the needle in this position will be :

A thin rectangular magnet suspended freely has a period of oscillation equal to $$T.$$ Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $$T^{\prime },$$ the ratio {{T'} \over T} is

The magnetic lines of force inside a bar magnet

The time period of satellite of earth is $$5$$ hours. If the separation between the earth and the satellite is increased to $$4$$ times the previous value, the new time period will become

The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ $$km/s.$$ If the body is projected at an angle of $$45^{\circ }$$ with the vertical, the escape velocity will be

Two spherical bodies of mass $$M$$ and $$5M$$ & radii $$R$$ & $$2R$$ respectively are released in free space with initial separation between their centers equal to $$12R$$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

To demonstrate the phenomenon of interference, we require two sources which emit radiation

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

The work done in placing a charge of $$8\times 10^{-18}$$ coulomb on a condenser of capacity $$100$$ micro-farad is

A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two rigid supports $$1$$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $$n.$$ The frequency $$n$$ of the alternating source is

The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by $y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres$ where $$x$$ is expressed in metres and $$t$$ in seconds. The speed of the wave - motion, in $$m{s}^{-1}$$, is

A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The beat frequency decreases to $$2$$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

A particle of mass $$M$$ and charge $$Q$$ moving with velocity $$\overrightarrow{v}$$ describe a circular path of radius $$R$$ when subjected to a uniform transverse magnetic field of induction $$B.$$ The network done by the field when the particle completes one full circle is

A particle of charge $$-16\times 10^{-18}$$ coulomb moving with velocity $$10m{s}^{-1}$$ along the $$x$$-axis enters a region where a magnetic field of induction $$B$$ is along the $$y$$-axis, and an electric field of magnitude $$10^{4}V/m$$ is along the negative $$z$$-axis. If the charged particle continues moving along the $$x$$-axis, the magnitude of $$B$$ is

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $$49$$ $$N,$$ when the lift is stationary. If the lift moves downward with an acceleration of $$5m/s^2$$, the reading of the spring balance will be

A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $$0.2$$. The weight of the block is

Three forces start acting simultaneously on a particle moving with velocity, $$\overrightarrow{v}.$$ These forces are represented in magnitude and direction by the three sides of a triangle $$ABC$$. The particle will now move with velocity

A rocket with a lift-off mass $$3.5\times 10^{4}kg$$ is blasted upwards with an initial acceleration of $$10m/s^2.$$ Then the initial thrust of the blast is

A light spring balance hangs from the hook of the other light spring balance and a block of mass $$M$$ $$kg$$ hangs from the former one. Then the true statement about the scale reading is