A mechanism consists of a part which is translated with a velocity u and a rod AB of length L and mass M hinged at A. The rod rotates about a horizontal axis through A with angular velocity $w$ . The kinetic energy of rod when it is vertical as shown is $\frac{1}{2} M u^{2} + \frac{1}{x} M L^{2} w^{2} + \frac{1}{2} M L w u$ . The value of $x$ is

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Detailed Solution

$K . E = \frac{1}{2} M {(U + \frac{l}{2} ω)}^{2} + \frac{1}{2} \frac{M l^{2}}{12} ω^{2} \frac{M l^{2} ω^{2}}{6} + \frac{1}{2} M u^{2} + \frac{1}{2} L u ω M$

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