A particle of mass 4 m explodes into three pi | vedclass

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

Question

(C) Initially,the particle of mass $4 m$ is at rest,so its initial momentum is zero.Let the velocity of the heavier mass $(2 m)$ be $\vec{v} = v_x \ha

Vedclass · Accepted Answer

$\sqrt{13} ms^{-1}$

Vedclass · Answer

(C) Initially,the particle of mass $4 m$ is at rest,so its initial momentum is zero.Let the velocity of the heavier mass $(2 m)$ be $\vec{v} = v_x \hat{i} + v_y \hat{j}$.According to the law of conservation of linear momentum,the total final momentum must be zero:$\vec{P}_{initial} = \vec{P}_{final} = 0$$m(4 \hat{i}) + m(6 \hat{j}) + 2m(v_x \hat{i} + v_y \hat{j}) = 0$Dividing by $m$:$4 \hat{i} + 6 \hat{j} + 2v_x \hat{i} + 2v_y \hat{j} = 0$Equating the components:$4 + 2v_x = 0 \Rightarrow v_x = -2 ms^{-1}$$6 + 2v_y = 0 \Rightarrow v_y = -3 ms^{-1}$The magnitude of the velocity of the heavier mass is:$v = \sqrt{v_x^2 + v_y^2} = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} ms^{-1}$

$A$ particle of mass $4 m$ explodes into three pieces of masses $m, m$ and $2 m$. The equal masses move along $X$-axis and $Y$-axis with velocities $4 ms^{-1}$ and $6 ms^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

Similar Questions

$A$ bulb of $100 \ W$ rating is connected with $220 \ V$ supply. The resistance of the bulb is . . . . . . .

If $z_1 = a + ib$ and $z_2 = c + id$ are complex numbers such that $|z_1| = |z_2| = 1$ and $R(z_1\overline{z_2}) = 0$,then the pair of complex numbers $w_1 = a + ic$ and $w_2 = b + id$ satisfies

Water rises in a capillary tube of radius $r$ to a height $h$. The mass of water in the capillary is $m$. What will be the mass of water that rises in a capillary tube of radius $\frac{r}{3}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module