A small block of mass m is placed on a wedge | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Consider the system of the block $(m)$ and the wedge $(M)$. Since all surfaces are frictionless and there are no external horizontal forces acting

Vedclass · Accepted Answer

None

Vedclass · Answer

(D) Consider the system of the block $(m)$ and the wedge $(M)$. Since all surfaces are frictionless and there are no external horizontal forces acting on the system,the horizontal momentum of the system is conserved.Let $v$ be the velocity of the block relative to the ground and $V$ be the velocity of the wedge relative to the ground at any instant.By conservation of horizontal momentum: $mv_x + MV = 0$,where $v_x$ is the horizontal component of the block's velocity.Also,the work-energy theorem states that the loss in potential energy of the block is equal to the gain in kinetic energy of the system (since the spring is not compressed at the start and we look for the velocity of the wedge as the block reaches the bottom,assuming the spring is not yet significantly involved in the energy balance or is negligible for the peak velocity of the wedge).Using the conservation of energy: $mgh = \frac{1}{2}mv^2 + \frac{1}{2}MV^2$.From momentum conservation,$V = -\frac{mv_x}{M}$.For the wedge to attain maximum velocity,we analyze the motion. The correct expression for the velocity of the wedge $M$ when the block $m$ reaches the bottom is $V = \sqrt{\frac{2m^2gh}{M(M+m)}}$.Comparing this with the given options,none of the expressions match the derived result. Thus,the correct option is $D$.

Similar Questions

$A$ small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mkv^{2}$ where $v$ is its speed. The maximum height attained by the ball is

Three identical particles are joined together by a thread as shown in the figure. All the three particles are moving on a smooth horizontal plane about point $O$. If the speed of the outermost particle is $v_0$,then the ratio of tension in the three sections of the thread is:

$A$ trolley of mass $5\,kg$ on a horizontal smooth surface is pulled by a load of mass $2\,kg$ by means of a uniform rope $ABC$ of length $2\,m$ and mass $1\,kg$. As the load falls from $BC = 0$ to $BC = 2\,m$,its acceleration in $m/s^2$ changes from:

Vedclass Test Series

Exam Paper Generator

Online Exam Module