Question

2019 ODISHA)
*
5. An object flying in air with velocity
(20î + 25j-12k) suddenly breaks in two pieces
whose masses are in the ratio 1:5. The smaller
mass flies off with a velocity (100î +35j+8k).
The velocity of the larger piece will be :-
(1) 4ỉ +23j - 16k
(2) -100ỉ – 35j – 8k
(3) 20î +15j-80k
(4) -20î – 15j - 80k
​

Answer 1

Let, mass of smaller piece is m.

So, mass of bigger piece is 5m.

Also, let velocity of bigger part is v.

Since, no external force is applied :

Initial momentum = Final momentum

( m + 5m )( 20i + 25j - 12k ) = m( 100i + 35j + 8k ) + 5mv

6( 20i + 25j - 12k ) = (100i + 35j + 8k) + 5v

5v = 120i + 150j - 72k - ( 100i + 35j + 8k )

5v = 20i + 115j - 80k

v = 4i + 23j - 16k

Therefore, velocity of the larger piece will be 4i + 23j - 16k.

Hence, this is the required solution.

Answer 2

Answer:

Let, mass of smaller piece is m.

So, mass of bigger piece is 5m.

Also, let velocity of bigger part is v.

Since, no external force is applied :

Initial momentum = Final momentum

( m + 5m )( 20i + 25j - 12k ) = m( 100i + 35j + 8k ) + 5mv

6( 20i + 25j - 12k ) = (100i + 35j + 8k) + 5v

5v = 120i + 150j - 72k - ( 100i + 35j + 8k )

5v = 20i + 115j - 80k

v = 4i + 23j - 16k

Therefore, velocity of the larger piece will be 4i + 23j - 16k.

Hence, this is the required solution.

Explanation: