MHTCET 11 Apr 2026 Shift 1 Paper

Concept:Power is delivered only by the tangential force, because the centripetal force acts perpendicular to the velocity and does no work.Explanation:For a particle moving in a circle of constant radius $r$, the centripetal acceleration is written as:$$a_{c} = \frac{v^{2}}{r}$$It is given that:$$a_{c} = k^{2} r t^{2}$$Equating the two expressions, we get:$$\frac{v^{2}}{r} = k^{2} r t^{2}$$Multiplying both sides by $r$, we get:$$v^{2} = k^{2} r^{2} t^{2}$$Taking the square root, the speed of the particle is:$$v = k r t$$Since the speed changes with time, the tangential acceleration is:$$a_{t} = \frac{dv}{dt} = k r$$The tangential force acting on the particle is:$$F_{t} = m a_{t} = m k r$$The centripetal force is always perpendicular to the velocity, so it does no work. Hence, the power delivered is due to the tangential force only:$$P = F_{t} \cdot v = (m k r)(k r t)$$Simplifying this expression, we get:$$P = m k^{2} r^{2} t$$Answer:The power delivered to the particle is $m k^{2} r^{2} t$. Hence, the correct option is B.