A uniform solid sphere rolls down a vertical surface without sliding. If the vertical surface moves with an acceleration $$a=g2$$, the minimum coefficient of friction between the sphere and vertical surfaces so as to prevent relative sliding is

Question

A uniform solid sphere rolls down a vertical surface without sliding. If the vertical surface moves with an acceleration $$a=g2$$, the minimum coefficient of friction between the sphere and vertical surfaces so as to prevent relative sliding is

Infinity Learn · Accepted Answer

Let sphere rolls down with acceleration a'. Writing force and torque equations for $$sphereN=mg2$$     .....(i)mg$$−$$f=ma$$′   ......$$(ii)fR=25mR2$$⋅α$$f=25mR$$α     .......$$(iii)α$$R=a$$′         .......(iv)⇒ $$f=25ma$$′ or a′$$=52fm$$        ........(v) from (ii) and (v) mg−$$f=52f$$⇒$$mg=72f$$ or $$f=27mg$$ But, f≤N hence $$27mg$$≤μ$$mg2$$⇒μ≥$$47$$

A uniform solid sphere rolls down a vertical surface without sliding. If the vertical surface moves with an acceleration $a = \frac{g}{2}$ , the minimum coefficient of friction between the sphere and vertical surfaces so as to prevent relative sliding is

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A uniform solid sphere rolls down a vertical surface without sliding. If the vertical surface moves with an acceleration a=g2, the minimum coefficient of friction between the sphere and vertical surfaces so as to prevent relative sliding is

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A uniform solid sphere rolls down a vertical surface without sliding. If the vertical surface moves with an acceleration $a = \frac{g}{2}$ , the minimum coefficient of friction between the sphere and vertical surfaces so as to prevent relative sliding is