Question

A massive horizontal platform is moving horizontally with a constant acceleration of $10m/s^2$ as shown in the figure. A particle $P$ of mass $m=1kg$ is kept at rest at the smooth surface as shown in the figure. The particle is hinged at $O$ with the help of a massless rod $OP$ of length $0.9m$. Hinge $O$ is fixed on the platform and the rod can freely rotate about point $O$. Now the particle $P$ is imparted a velocity in the opposite direction of the platform's acceleration such that it is just able to complete the circular motion about point $O$. Then the maximum tension appearing in the rod during the motion is $10n$. Find the value of $n$.

Answer 1

Answer: 5.00

Relative to plate velocity imparted to particle is $V$.

$0-\frac{1}{2}m{v}^2=-ma\ell$
$v^2=2a\ell$
Tension is maximum at point $B$
$T-ma=\frac{m{v}_1^2}{\ell }$
$T=ma+\frac{m{v}_1^2}{\ell }$
$ma\ell =\frac{1}{2}m{v}_1^2-\frac{1}{2}m{v}^2$
$\frac{1}{2}m{v}_1^2=ma\ell +\frac{1}{2}m\times 2a\ell$
$v_1^2=4a\ell$
$T=ma+\frac{m}{\ell }\times 4a\ell$
$T=5ma=5\times 1\times 10=50N$