Question

A mass of $2.9kg$ is suspended from a string of length $50cm$ and is at rest. Another body of mass $100g$, which is moving horizontally with a velocity of $150m/s$ strikes and sticks to it. Subsequently, when the string makes an angle of ${60}^o$ with the vertical, the tension in the string is:
($g=10m/s^2$)

• A. $140N$
• B. $135N$
• C. $125N$
• D. $90N$

Answer 1

The correct option is B $135N$

Since the collision is perfectly inelastic, conserving momentum, we get,

$0.1\times 150=(2.9+0.1)\times u$

$u=5m/s$

After this, applying conservation of energy,

$(m+M)g\left(l\right(1-cos\left(60\right))+\frac{1}{2}(m+M)v^2=\frac{1}{2}(m+M)u^2$

$\frac{1}{2}(m+M)v^2=\frac{1}{2}(m+M)u^2-(m+M)gl(1-cos(60\left)\right)$

$(m+M)v^2=3\times 5^2-2\times 3\times 10\times 0.5\times (1-0.5)$

$⟹(m+M)v^2=60$

$T=(m+M)gcos\left(\theta \right)+(m+M)v^2/l$
$=15+120$

$T=135N$