In an inelastic collision an electron excites a hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-shell state and ionizes it. At least how much energy the second electron transfers to the atom in the M-shell state ?

• + 3.4 eV

• + 1.51 eV

• − 3.4 eV

• − 1.51 eV

Given $\overrightarrow{\mathrm{A}} = 2 \hat{\mathrm{i}} + 3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}} = \hat{\mathrm{i}} + \hat{\mathrm{j}}$. The component of vector $\overrightarrow{\mathrm{A}}$ along vector $\overrightarrow{\mathrm{B}}$ is

• $\frac{1}{\sqrt{2}}$

• $\frac{3}{\sqrt{2}}$

• $\frac{5}{\sqrt{2}}$

• $\frac{7}{\sqrt{2}}$

A cubical vessel of height 1 m is full of water. What is the amount of work done in pumping water out of the vessel ? (Take g = 10 m/s²)

• 1250 J

• 5000 J

• 1000 J

• 2500 J

If a person can throw a stone to maximum height of h metre vertically, then the maximum distance through which it can be thrown horizontally by the same person is

• $\frac{\mathrm{h}}{2}$

• h

• 2h

• 3h

A body of mass 6 kg is acted upon by a force which causes a displacement in it given by $\mathrm{x} = \frac{{\mathrm{t}}^2}{4}$metre, where t is the time in second. The work done by the force in 2 s is

• 12 J

• 9 J

• 6 J

• 3 J

A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

• t^1/2

• t^3/4

• t^3/2

• t²

A particle is moving with a constant speed v in a circle. What is the magnitude of average velocity after half  rotation ?

• 2v

• $2\frac{\mathrm{v}}{\mathrm{\pi }}$

• $\frac{\mathrm{v}}{2}$

• $\frac{\mathrm{v}}{2\mathrm{\pi }}$

A cricket ball of mass 0.25 kg with speed 10 m/s collides with a bat and returns with same speed within 0.01 s. The force acted on bat is

• 25 N

• 50 N

• 250 N

• 500 N

If the earth were to suddenly contract to $\frac{1}{\mathrm{n}}\mathrm{th}$ of its present radius without any change in its mass, the duration of the new day will be nearly

• 24/n h

• 24 n h

• 24/n² h

• 24 n² h

If g is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth is

• $\frac{\mathrm{mgR}}{4}$

• $\frac{\mathrm{mgR}}{2}$

• mgR

• 2mgR