A spaceship in space sweeps stationary interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv²(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period T₁ and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T₂. The ratio $${{{T_1}} \over {{T_2}}}$$ will be :

A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _______.

The surface of a metal is illuminated alternately with photons of energies E₁ = 4 eV and E₂ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _____.