Work Power and Energy 3 Question 10
10. In the figures (a) and (b) $A C, D G$ and $G F$ are fixed inclined planes, $B C=E F=x$ and $A B=D E=y$. A small block of mass $M$ is released from the point $A$. It slides down $A C$ and reaches $C$ with a speed $v _C$. The same block is released from rest from the point $D$. It slides down $D G F$ and reaches the point $F$ with speed $v _F$. The coefficients of kinetic frictions between the block and both the surfaces $A C$ and $D G F$ are $\mu$. Calculate $v _C$ and $v _F$.
$(1980,6 M)$
(a)
(b)
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Answer:
Correct Answer: 10. $v _C=v _F=\sqrt{2(g y-\mu g x)}$
Solution:
- In both the cases, work done by friction will be $-\mu M g x$.
$$ \begin{array}{rlrl} \therefore & \frac{1}{2} M v _C^{2} & =\frac{1}{2} M v _F^{2} \\ & =M g y-\mu M g x \\ \therefore & v _C & =v _F=\sqrt{2 g y-2 \mu g x} \end{array} $$
