Question

JEE MAINS PHYSICS QUESTION SEPTEMBER 2020

Answer 1

A rocker moving in free space has varying mass due to fuel exhausted as dm(t)/dt = -bv²(t)

where m(t) = instantaneous mass

b = constant

v(t) = instantaneous velocity.

To find : if gases are ejected with velocity u, with respect to rocket, instantaneous acceleration of rocket should be.....

solution : according to Newton's second law,

F = ma

= m × du/dt

= dm/dt × u

= u(dm/dt)

so force in term of rate of change of mass is given by, F = ma = u(dm/dt)

here dM(t))dt = -bv²(t)

so, F = u × -bv²(t) = -ubv²(t)

⇒ma = -ubv²(t)

⇒a = -ubv²(t)/m(t)

Therefore the correct option is (1) ubv²(t)/m(t)