SATHEE: Work Power and Energy 3 Question 10

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 $μ$ . Calculate $v_{C}$ and $v_{F}$ .

$(1980, 6 M)$

(a)

(b)

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Answer:

Correct Answer: 10. $v_{C} = v_{F} = \sqrt{2 (g y - μ g x)}$

Solution:

In both the cases, work done by friction will be $- μ M g x$ .

$\begin{aligned} ∴ & \frac{1}{2} M v_{C}^{2} & = \frac{1}{2} M v_{F}^{2} \\ = M g y - μ M g x \\ ∴ & v_{C} & = v_{F} = \sqrt{2 g y - 2 μ g x} \end{aligned}$

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Work Power and Energy 3 Question 10

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