A shell of mass 5M, acted upon by no external force and initially at rest, bursts into three fragments of masses M, 2M and 2M respectively. The first two fragments move in opposite directions with velocities of magnitudes 2v and v respectively. The third fragment will

Question

A shell of mass 5M, acted upon by no external force and initially at rest, bursts into three fragments of masses M, 2M and 2M respectively. The first two fragments move in opposite directions with velocities of magnitudes 2v and v respectively. The third fragment will (A) move with a velocity v in a direction perpendicular to the other two (B) move with a velocity 2v in the direction of velocity of the first fragment (C) be at rest (D) move with a velocity v in the direction of velocity of the second fragment

Tardigrade Admin · Accepted Answer

Let the velocity of third fragment is v. Then by the conservation of linear momentum 5(0)=M × 2 v -2 M × v+2 M × v prime ⇒ v prime=0

Q. A shell of mass $5 M$ , acted upon by no external force and initially at rest, bursts into three fragments of masses $M, 2 M$ and $2 M$ respectively. The first two fragments move in opposite directions with velocities of magnitudes $2 v$ and $v$ respectively. The third fragment will

move with a velocity $v$ in a direction perpendicular to the other two

move with a velocity $2 v$ in the direction of velocity of the first fragment

be at rest

move with a velocity $v$ in the direction of velocity of the second fragment

Let the velocity of third fragment is $v$ . Then by the
conservation of linear momentum
$5 (0) = M \times 2 v - 2 M \times v + 2 M \times v^{'}$
$\Rightarrow v^{'} = 0$

Q. A shell of mass 5M, acted upon by no external force and initially at rest, bursts into three fragments of masses M,2M and 2M respectively. The first two fragments move in opposite directions with velocities of magnitudes 2v and v respectively. The third fragment will

move with a velocity v in a direction perpendicular to the other two

move with a velocity 2v in the direction of velocity of the first fragment