A body of mass m moving along a straight line | vedclass

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

Question

(B) Let the initial velocity of the body of mass $m$ be $v$. The initial kinetic energy is $K_i = \frac{1}{2}mv^2$.By the law of conservation of linea

Vedclass · Accepted Answer

$2/3$

Vedclass · Answer

(B) Let the initial velocity of the body of mass $m$ be $v$. The initial kinetic energy is $K_i = \frac{1}{2}mv^2$.By the law of conservation of linear momentum: $mv + (2m)(0) = (m + 2m)v'$,where $v'$ is the final common velocity.$mv = 3mv' \implies v' = v/3$.The final kinetic energy is $K_f = \frac{1}{2}(m + 2m)(v')^2 = \frac{1}{2}(3m)(v/3)^2 = \frac{1}{2}(3m)(v^2/9) = \frac{1}{6}mv^2$.The loss in kinetic energy is $\Delta K = K_i - K_f = \frac{1}{2}mv^2 - \frac{1}{6}mv^2 = \frac{3-1}{6}mv^2 = \frac{2}{6}mv^2 = \frac{1}{3}mv^2$.The fraction of kinetic energy lost is $\frac{\Delta K}{K_i} = \frac{\frac{1}{3}mv^2}{\frac{1}{2}mv^2} = \frac{1}{3} 	imes 2 = 2/3$.

$A$ body of mass $m$ moving along a straight line collides with a stationary body of mass $2m$. After collision,if the two bodies move together with the same velocity,then the fraction of kinetic energy lost in the process is

Similar Questions

$A$ body of mass $m$ moving with speed $3 \ m/s$ collides with a body of mass $2m$ at rest. The coalesced mass will start to move with a speed of (in $m/s$)

$A$ body of mass $20 \ kg$ moving with a speed of $10 \ m/s$ collides with a stationary body of mass $5 \ kg$. After the collision,both bodies stick together. The combined kinetic energy of the system will be $...... \ J$.

$A$ body of mass $4\, kg$ moving with velocity $12\, m/s$ collides with another body of mass $6\, kg$ at rest. If two bodies stick together after collision,then the loss of kinetic energy of the system is .............. $J$.

Two balls of masses $m$ each are moving at right angles to each other with velocities $6 \, m/s$ and $8 \, m/s$ respectively. If the collision between them is perfectly inelastic,the velocity of the combined mass is ......... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module