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Q.

A worker wishes to pile up sand on to a circular area of radius R. No sand is to spill on to the surrounding area. If μs is the coefficient of static friction between sand particles, then choose the correct statement(s).

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a

The greatest height of sand pile that can be created is μs R.

b

The greatest height of sand pile that can be created is R/μs .

c

Minimum work required create greatest height sand pile is  π12μs2R4ρg. Where ρ is the density of sand volume

d

Sand pile will be in stable equilibrium.

answer is A.

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Detailed Solution

From free body diagram of sand particle  tanθ=μs=h/R----(1)COM of solid cone is at height h4 from base.Work required  =13πR2hρgh4---(2) from (1) and (2) W=13πR2ρgμs2R24The system is in unstable equilibrium.
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