The force on a hemisphere of radius $1\, cm$ if a parallel beam of monochromatic light of wavelength $500\, nm$ falls on it with an intensity of $0.5\, W/cm^2$,striking the curved surface in a direction which is perpendicular to the flat face of the hemisphere is (assume the collisions to be perfectly inelastic).

Find the compression in the spring with spring constant $K = 5 \ N/m$ which is attached to a metal plate of area $50 \ m^2$. Light of intensity $I = 40 \ MW/m^2$ is incident at an angle of $60^o$ on the metal plate,and the coefficient of reflection is $\rho = 0.5$ for the plate. (in $m$)

Radiation of intensity $I$ is falling obliquely on a surface. The area of the surface exposed to radiation is $A$. The angle of incidence with the normal is $\theta$. Select the correct alternative,where $\beta$ is a constant that depends upon the nature of the surface.

$A$ light bulb of power $100 \ W$ is placed at the centre of a hollow sphere of radius $10 \ cm$. If $66\%$ of the energy is converted into light,then the pressure exerted by the light on the surface of the sphere will be (Assume the surface of the sphere to be perfectly absorbing).

An impulse laser may be treated as a source of photons that are emitted during the time interval of the pulse,which is followed by a time interval when no photons are produced. Pulses are periodically repeated. $A$ laser beam of diameter $d = 10 \, \mu m$ is directed upward and is perpendicular to the thin foil surface which has a reflection coefficient $\rho = 0.50$ (see the sketch of the experiment). The reflection coefficient of the surface is the ratio of the reflected energy to the incident energy. $A$ pulse with duration of $0.13 \, ms$ has a total energy of $10 \, J$. What is the mass of the piece of foil that can be supported in the air solely by the light pressure of the laser beam? (Take $g = 10 \, m/s^2$)

An astronaut floating freely in space decides to use his flashlight as a rocket. He shines a $10$ $W$ light beam in a fixed direction so that he acquires momentum in the opposite direction. If his mass is $80$ kg,how long must he shine the light to reach a velocity of $1$ $m/s$?