A girl of mass 50 ,kg is swinging on a cradle | vedclass

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(C) The power $P$ generated by a force $\vec{F}$ acting on an object moving with velocity $\vec{v}$ is given by $P = \vec{F} \cdot \vec{v} = Fv \cos \

Vedclass · Accepted Answer

$490 \sqrt{3} \,W$

Vedclass · Answer

(C) The power $P$ generated by a force $\vec{F}$ acting on an object moving with velocity $\vec{v}$ is given by $P = \vec{F} \cdot \vec{v} = Fv \cos 	heta$, where $	heta$ is the angle between the force vector and the velocity vector.Here, the gravitational force $\vec{F} = m\vec{g}$ acts vertically downwards.The velocity vector $\vec{v}$ makes an angle of $60^{\circ}$ with the vertical.Since the force is downwards and the velocity is directed upwards at an angle of $60^{\circ}$ with the vertical, the angle $	heta$ between the force vector and the velocity vector is $180^{\circ} - 60^{\circ} = 120^{\circ}$.Given: $m = 50 \,kg$, $v = 2 \,ms^{-1}$, $g = 9.8 \,ms^{-2}$.$P = mgv \cos(120^{\circ})$$P = 50 	imes 9.8 	imes 2 	imes (-0.5)$$P = 980 	imes (-0.5) = -490 \,W$.The magnitude of the power generated by gravity is $490 \,W$. However, considering the options provided and the standard interpretation of such problems where the component of gravity opposing the motion is considered, the magnitude is $490 \,W$. If the question asks for the power generated by the girl (against gravity), it would be $490 \,W$. Given the options, $490 \,W$ is not explicitly listed, but $490 \sqrt{3} \,W$ is often associated with the component $mg \cos(30^{\circ})$ or similar. Re-evaluating the geometry: the angle between the vertical and the velocity is $60^{\circ}$. The component of gravity acting against the velocity is $mg \cos(180-60) = mg \cos(120) = -0.5 mg$. The magnitude is $0.5 	imes 50 	imes 9.8 	imes 2 = 490 \,W$. Since $490 \,W$ is not an option, and $490 \sqrt{3} \,W$ is provided, there might be a geometric misinterpretation in the source. Based on standard physics, the answer is $490 \,W$.

$A$ girl of mass $50 \,kg$ is swinging on a cradle. If she moves with a velocity of $2 \,ms^{-1}$ in a direction making an angle of $60^{\circ}$ with the vertical, then the power generated by the gravitational force is $\left(g=9.8 \,ms^{-2}\right)$.

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