Question

The length of a ballistic pendulum is $1m$ and mass of its block is $1.9kg$. A bullet of mass $0.1kg$ strikes the block of ballistic pendulum in horizontal direction with a velocity $100m{s}^{–1}$ and got embedded in the block. After collision the combined mass (block & bullet) swings away from lowest point. The tension in the string when it makes an angle $60°$ with vertical is $(g=10m{s}^{-2})$:

• A. $20N$
• B. $30N$
• C. $40N$
• D. $50N$

Answer 1

The correct option is C $40N$

Momentum Conservation
$0.1\times 100=(1.9+0.1)V_o$
$V_o=5m{s}^{-1}.$
$H=L(1-cos{60}^{\circ }).=\frac{1}{2}=\frac{1}{2}m.$

Energy Conservation
$\frac{1}{2}\left(2\right)(5{)}^2=\frac{1}{2}\times 2\times V^2+2\times 10\times \frac{1}{2}$
$25-10=V^2.$
$V=\sqrt{15}mvs$

By Force Balance

$T-mgcos{60}^{\circ }=m\frac{V^2}{L}.$
$T=2\times 10\times \frac{1}{2}+2\times \frac{15}{1}$
$=40N.$