Question

A bullet of mass $10$g moving horizontally at a speed of $140$m$/$s strikes a block of mass $100$g attached to a string like a simple pendulum. The bullet penetrates the block and emerges then on the other side. If the block rises by $80$cm, then find the final velocity of bullet.

• A. $80m/s$
• B. $100m/s$
• C. $120m/s$
• D. $140m/s$

Answer 1

The correct option is B $100m/s$

Let the speed of the bullet be $v_1$. Let the common velocity of the bullet and the block, after the bullet is attached like a simple pendulum is $v_2$.

By the principle of conservation of linear momentum

$\frac{10}{1000}\times 140+\frac{100}{1000}\times 0$

$=\frac{100}{1000}{v}_1+\frac{10}{1000}{v}_2$

$140=10v_1+v_2$ ..........(i)

For the block, $0=v_1^2-2g\left(\frac{80}{100}\right)$

$\Rightarrow v_1=4m/s$

$\Rightarrow 140=10\times 4+v_2$ [from Eq. (i)]

$\Rightarrow v_2=100m/s$

Final velocity of bullet $=100m/s$.