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A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the speed of both is related as :
A
$V_B \gt V_m$
B
$V_B \lt V_m$
C
$V_B = V_m$
D
$V_B$ and $V_m$ can't be related
Detailed Solution
On a frictionless incline only gravity does work (the normal force does no work).
By conservation of energy, for both the man and the bag: $mgh = \dfrac{1}{2}mv^2 \Rightarrow v = \sqrt{2gh}$
The speed depends only on the height fallen, not on the path or the mass. (The times taken are different.)
So $V_B = V_m$.
By conservation of energy, for both the man and the bag: $mgh = \dfrac{1}{2}mv^2 \Rightarrow v = \sqrt{2gh}$
The speed depends only on the height fallen, not on the path or the mass. (The times taken are different.)
So $V_B = V_m$.