Question

A particle of mass m is given initial horizontal velocity of magnitude u as shown in the figure. It transfers to the fixed inclined plane without a jump, that is, its trajectory changes sharply from the horizontal line to the inclined line. All the surfaces are smooth and ${90}^0\ge \theta >0^0.$ Then the height to which the particle shall rise on the inclined plane (assume the length of the inclined plane to be very large)

• A. increases with increase in $\theta$
• B. decreases with increase in $\theta$
• C. is independent of $\theta$
• D. data insufficient

Answer 1

Answer: (B)

decreases with increase in $\theta$

Just before the particle transfers to inclined surface, we resolve its velocity along and normal to the plane. Momentum will be conserved but energy conservation is not valid as the trajectory changes sharply.
For the trajectory of the particle to sharply change from the horizontal line to the inclined line, the impact of the particle with inclined plane should reduce the usin $\theta$ component of velocity to zero. Hence the particle moves up the incline with speed u cos $\theta$. Hence as $\theta$ increases, the height to which the particle rises shall decrease.