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  • A solid cube is placed on a horizontal on a horizontal surface. The coefficient of friction between them is μ where μ<1/2. A variable horizontal on the cube's upper face

A solid cube is placed on a horizontal on a horizontal surface. The coefficient of friction between them is μ where μ<1/2. A variable horizontal on the cube's upper face, perpendicular to one edge and passing through the the mid-point of edge, as shown in figure. The maximum acceleration with which it can move without toppling is

 

Option: 1

\frac{g}{2} \times(1-\mu)


Option: 2

\frac{g}{2} \times(1+\mu)


Option: 3

g


Option: 4

2 \mathrm{g}


Answers (1)

best_answer

Drawing FBD of situation from side view 

Balancing clockwise and anticlockwise torque at 0

P a=\frac{m g a}{2}                                      \text { ( } a \rightarrow \text { side of cube) }

\Rightarrow \quad P=m g / 2          -\text { (1) }

Now; Applying NLM on cube:-

                       P-\mu N=m a_{\text {max }}

                      \frac{m g}{2}-\mu m g=m a_{\text {max }}

                     \Rightarrow \quad a_{\text {max }}=g / 2(1-\mu)

Posted by

Suraj Bhandari

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