A particle of mass 3m is projected from the g | vedclass

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

Question

(C) The center of mass of the system follows the original parabolic trajectory because the explosion is caused by internal forces.The horizontal range

Vedclass · Accepted Answer

$\frac{5R}{4}$

Vedclass · Answer

(C) The center of mass of the system follows the original parabolic trajectory because the explosion is caused by internal forces.The horizontal range of the center of mass is $R$,so it lands at $x_{com} = R$.The highest point of the trajectory is at a horizontal distance of $\frac{R}{2}$ from the point of projection.Let the smaller mass $m$ come to rest,meaning its horizontal position is $x_1 = \frac{R}{2}$.Let the larger mass $2m$ fall at a distance $x_2 = x$.The center of mass position is given by $x_{com} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$.Substituting the values: $R = \frac{m \cdot \frac{R}{2} + 2m \cdot x}{m + 2m}$.$3mR = \frac{mR}{2} + 2mx$.$3mR - \frac{mR}{2} = 2mx$.$\frac{5mR}{2} = 2mx$.$x = \frac{5R}{4}$.

Similar Questions

$A$ man weighing $80\, kg$ is standing at the centre of a flat boat and he is $20\, m$ from the shore. He walks $8\, m$ on the boat towards the shore and then halts. The boat weighs $200\, kg$. How far is he from the shore at the end of this time?

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5 \ m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. (in $m$)

Two particles $X$ and $Y$,initially at rest,move towards each other under mutual attraction. If at any instant the velocity of particle $X$ is $V$ and the velocity of particle $Y$ is $2V$,then the velocity of their center of mass will be:

Two balls are thrown in the air. The second ball is thrown $2 \ s$ after the first ball. What is the acceleration of the center of mass of the two balls while they are in the air?

Two particles of masses $2 \ kg$ and $3 \ kg$ are moving along the $X$-axis with velocities $3 \ m/s$ and $2 \ m/s$ respectively. The velocity of the center of mass of this system is ........ $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module