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A plank of mass m rests symmetrically on two wedges B and C of

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A plank of mass $m$ rests symmetrically on two wedges $B$ and $C$ of mass $M$ . What is the acceleration of the plank? Neglect the friction between all the contact surfaces.

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Updated on: Jun 26, 2023

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A plank of mass

m

rests symmetrically on two wedges

B

and

C

of mass

M

. What is the acceleration of the plank? Neglect the friction between all the contact surfaces.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

When the plank is released, let it fall through a distance

y

and let both the wedges move through a distance

x

y = x tan θ .......(i)

On differentiating this expression twice, we obtain

a = A tan θ FBD

of rod and wedge :

\sum F_{x} = N sin θ = M A \dots .. (ii) \sum F_{y} = N^{'} - N cos θ = M g = 0...

Equations of plank:

\sum F_{x} = N sin θ - N sin θ = 0 \dots \sum F_{y} = mg - 2 N cos θ = m \dots\dots

From (ii),

N = \frac{MA}{s i n θ}

On substituting expression for

N

and

a

in (v), we obtain

\Rightarrow mg - \frac{2 MA cos θ}{sin θ} = \frac{mA sin θ}{cos θ} A = \frac{mg sin θ cos θ}{m ^{2} sin ^{2} θ + 2 M cos ^{2} θ}

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Question Text	A plank of mass $m$ rests symmetrically on two wedges $B$ and $C$ of mass $M$ . What is the acceleration of the plank? Neglect the friction between all the contact surfaces.
Updated On	Jun 26, 2023
Topic	Laws of motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	623
Avg. Video Duration	9 min

A plank of mass $m$ rests symmetrically on two wedges $B$ and $C$ of mass $M$ . What is the acceleration of the plank? Neglect the friction between all the contact surfaces.

Text solutionVerified

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A plank of mass m rests symmetrically on two wedges B and C of mass M. What is the acceleration of the plank? Neglect the friction between all the contact surfaces.

Text solutionVerified

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A plank of mass $m$ rests symmetrically on two wedges $B$ and $C$ of mass $M$ . What is the acceleration of the plank? Neglect the friction between all the contact surfaces.