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Relation between Work Done and PE

A solid spher...

Question

A solid sphere of mass 0.50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is $\frac{2}{7}$ . What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface ?

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Solution

If we take moment about the center than

$F \times R = I α + f \times R$

$\Rightarrow F = \frac{2}{5} m R α + μ m g$ ...(1)

$Again, F = m a_{c} - m m g$ ...(2)

$[b e c a u s e a_{c} = r α]$

$\Rightarrow a = \frac{(F + μ m g)}{m}$

\(\text{Putting the value of}a_c \text{in equation}(1),

$we get,$

= $(\frac{2}{5}) \frac{(F + μ m g)}{m} + μ m g$

$\Rightarrow= (\frac{2}{5}) (F + μ m g) μ m g$

$F = \frac{2}{5} F + \frac{2}{5} + \frac{2}{5} \times \times \frac{2}{7} \times 0.5 \times 10 + 2.7 \times 0.5 \times 10$

$\Rightarrow \frac{3 F}{5} = \frac{4}{7} + \frac{10}{7} = 2$

$\Rightarrow F = \frac{(5 \times 2)}{3} = \frac{10}{3} = 3.3 N$

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