A body of mass M at rest explodes into three | vedclass

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

Question

(B) The masses of the three pieces are $m_1 = \frac{M}{4}$,$m_2 = \frac{M}{4}$,and $m_3 = \frac{2M}{4} = \frac{M}{2}$.Since the initial body is at res

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(B) The masses of the three pieces are $m_1 = \frac{M}{4}$,$m_2 = \frac{M}{4}$,and $m_3 = \frac{2M}{4} = \frac{M}{2}$.Since the initial body is at rest,the total initial momentum is zero. By the law of conservation of linear momentum,the final total momentum must also be zero: $\vec{P}_1 + \vec{P}_2 + \vec{P}_3 = 0$.This implies $\vec{P}_3 = -(\vec{P}_1 + \vec{P}_2)$.The magnitudes of the momenta of the two smaller pieces are $P_1 = m_1 v_1 = \frac{M}{4} 	imes 30 = 7.5M$ and $P_2 = m_2 v_2 = \frac{M}{4} 	imes 40 = 10M$.Since $\vec{P}_1$ and $\vec{P}_2$ are perpendicular,the magnitude of their resultant is $P_{12} = \sqrt{P_1^2 + P_2^2} = \sqrt{(7.5M)^2 + (10M)^2} = \sqrt{56.25M^2 + 100M^2} = \sqrt{156.25M^2} = 12.5M$.Since $\vec{P}_3 = -(\vec{P}_1 + \vec{P}_2)$,the magnitude $P_3 = P_{12} = 12.5M$.Given $P_3 = m_3 v_3 = \frac{M}{2} v_3$,we have $\frac{M}{2} v_3 = 12.5M$.Solving for $v_3$,we get $v_3 = 12.5 	imes 2 = 25 \, m/s$.

$A$ body of mass $M$ at rest explodes into three pieces,in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, m/s$ and $40 \, m/s$ respectively. The velocity of the third piece will be ............... $\, m/s$.

Similar Questions

$A$ person of mass $80 \ kg$ is standing on a trolley of mass $320 \ kg$. The trolley is at rest on a frictionless horizontal rail. If the person walks on the trolley at a speed of $1 \ m/s$,what will be their displacement relative to the ground after $4 \ s$?

$A$ machine gun of mass $10\,kg$ fires $20\,g$ bullets at the rate of $180$ bullets per minute with a speed of $100\,m s^{-1}$ each. The recoil velocity of the gun is $.............\,m/s$.

State the law of conservation of total linear momentum for a system of particles.

$A$ man of mass $m_1$ is standing at a height $h$ from the floor in a gravity-free room. He throws a ball of mass $m_2$ downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the floor.

$A$ bomb at rest in the air explodes into two fragments. If one fragment moves vertically upwards with a velocity $v_0$,in which direction will the other fragment move?

Vedclass Test Series

Exam Paper Generator

Online Exam Module