TS EAMCET 9-Sep-2020 Shift 1 Solved Paper

Bullet hits block and gets lodged into the block. After this, block + bullet system moves to rise upto height h
Let, v = common velocity of block and bullet with which mass system begins to rise.
This is an example of perfectly inelastic collision, hence according to conservation of linear momentum,
⇒‌‌mv0=(m+M)v
So, ‌‌v=‌

mv0

(m+M)

∴ Loss of KE
= Final KE of system - Initial KE of bullet
=‌

1

2

(m+M)v2−‌

1

2

mv02
=‌

1

2

(m+M)‌

m2v02

(m+M)2

−‌

1

2

mv02
=‌

1

2

mv02(‌

m

m+M

−1)

=‌

1

2

mv02(‌

M

m+M

)