A uniform rod of mass M and length L is hinged at lower end on a table. The rod can rotate freely in vertical plane and there is no friction at the hinge. A uniform solid ball of mass M and radius $R= \frac{L}{3}$ is placed in contact with the vertical rod and a horizontal force F is applied at the upper end of the rod. There is no friction between rod and the ball and there is sufficient friction between ball and ground for pure rolling. Mark the correct statement(s).

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The acceleration of centre of mass of ball just after the application of force is $\frac{15}{22} \frac{F}{M}$ .

The horizontal component of hinge reaction on the rod just after application of force is $\frac{44}{43} F$

The horizontal component of hinge reaction on the rod just after application of force is $\frac{43}{44} F$

The angular acceleration of rod just after the application of force is $\frac{45}{22} \frac{F}{ML}$

answer is A, B, C.

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Detailed Solution

For ball: $N . R = \frac{7}{5} M R^{2} \frac{a_{0}}{R}$
$\Rightarrow N = \frac{7}{5} M a_{0} (i)$
For rod: $(F - \frac{N}{3}) L = \frac{M L^{2}}{3} α (i i)$
$A l s o, \frac{L α}{3} = a_{0} (i i i) F r o m (i), (i i) & (i i i) a_{0} = \frac{15}{22} \frac{F}{M}; α_{0} = \frac{45 F}{22 M L}$

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