Q.27. A stick of mass m and length l is pivoted at one end and is displaced through an angle $\theta$. The
increase in potential energy is

(1) $mg\frac{l}{2}\left(1-\cos \theta \right)$
(2) $mg\frac{l}{2}\left(1+\cos \theta \right)$
(3) $mg\frac{l}{2}\left(1-\sin \theta \right)$
(4) $mg\frac{l}{2}\left(1+\sin \theta \right)$

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 The potential energy of a particle of mass 5 kg moving in x-y plane is given by equation, U = –7x + 24y joule. Here x and y are in metre at t = 0, the particle is at origin and moving with velocity ( ˆˆ 23 ij + ) m/s. The magnitude of acceleration of particle is
(1) 3 m/s2 (2) 5 m/s2 (3) 31 m/s2 (4) 15 m/s2