Suppose a block of mass `1kg` is placed over a rough surface and a horizontal force `F` is applied on the block as shown in figure. Now, let us see what are the values of force of friction `f` and acceleration of the block a if the force `F` is gradually increased. Given that `mu_(s) =0.5,mu_(k) =0.4 and g=10m//s^(2)`

Options

A. 16
B. 8
C. 4
D. 2

Answer

C

Explanation

The terminal velocity is given by v, where `v prop r^2`
(r = radius of the sphere).
The mass of the sphere can be given by m `=4/3pir^3rho`.
thus `m prop r^3`
So , according to the question,
`m_1/m_2 = 1/8 = (r_1/r_2)^3 rArr r_1/r_2 = 1/2`
and since , `v_1/v_2 = (r_1/r_2)^2 = (1/2)^2 = 1/4 = v/(nv) = 1/4 rArr n= 4`