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As shown here, in the figure, a cart C moving with acceleration 'b'. If the coefficient of friction between the block A and the cart is \mu then what is the maximum value of 'b' so that the block A does not fall.

 

Option: 1

\mu g


Option: 2

\mu ^2g


Option: 3

\frac{g}{}\mu


Option: 4

\frac{g}{}{\mu^2}


Answers (1)

best_answer

 

 

Sticking of a Block With Accelerated Cart -

While solving with the help of the concept of pseudo force.

When a cart moves with some acceleration toward right then a pseudo force (ma) acts on block toward left.

This force (ma) is an action force by a block on the cart. 

 

Now block will remain static w.r.t. block. If friction force= μR≥mg

For equilibrium condition

\mu ma\geq mg

a\geq \frac{g}{\mu}

R = ma

\therefore\ \; a_{min}=\frac{g}{\mu}

    F_{min}=(M+m)\frac{g}{\mu}

Pseudo force (ma) acts on block towards left

Fmin = Minimum force

amin = minimum acceleration cart

M, m are masses of the cart and block respectively

So, by using this concept -                                                

 Force acting on block A

W = f_L = mg = \mu(mb) \Rightarrow b = \frac{g}{\mu}

 

 

 

Posted by

Ritika Kankaria

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