Question

 A body of mass m=10⁻² kg is moving in a medium and experiences a frictional force F=−kv². Its initial speed is v₀= 10 ms⁻¹. If, after 10 s, its energy is ⅛ mv₀², the value of k will be 

(a) 10⁻³ kg m−1

(b) 10⁻³ kg s−1

(c) 10⁻⁴ kg m−1

(d) 10⁻¹ kg m−1 s−1

Answer 1

 (c) 10⁻⁴ kg m−1 is the correct answer 

Mass m = 10² Kg

Initial velocity v₀= 10 ms⁻¹

Time t = 10 s

Frictional Force F=− kv²

1/2 mv_f² = ⅛ mv₀²

v_f = v₀ /2

v_f = 10 /2 = 5 m/s

Now, the force is

(10^-2)dv/dt = -kv² 

\(\int ^5_{10} {dv\over v^2}=-100k\int^{10}_0 dt\) 

\({1\over5}={1\over10}=100k\times 10\) 

\(k=10^{-4} \space {kg \over m}\)