Sticking of a Block With Accelerated Cart
Category : JEE Main & Advanced
When a cart moves with some acceleration toward right then a pseudo force (ma) acts on block toward left.
This force (ma) is action force by a block on cart.
Now block will remain static w.r.t. cart. If friction force \[\mu R\ge mg\]
\[\Rightarrow \] \[\mu ma\ge mg\] \[[\text{As}\,R=ma]\]
\[\Rightarrow \] \[a\ge \frac{g}{\mu }\]
\[\therefore \] \[{{a}_{\min }}=\frac{g}{\mu }\]
This is the minimum acceleration of the cart so that block does not fall.
and the minimum force to hold the block together
\[{{F}_{\min }}=(M+m)\,{{a}_{\min }}\]
\[{{F}_{\min }}=(M+m)\,\frac{g}{\mu }\]
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