A carpenter exerts a force of magnitude 1.5 N at right angles to the surface of a nail of mass 3 gram to drive it into the wood. If wood offers a resistive force of 0.6 N and the time of interaction of hammer and the nail 0.01 s, the depth through which the nail penetrates is
(a) 15m
(b) 1.5 cm
(c) 15 cm
(d) 1.5 mm

Dear Student,
Net force acting on wood = 1.5 - 0.6
                                              => 0.9N

Mass of nail = 3 gm => 0.003 kg

Using, F = ma

a = F/m
a = 0.9 / 0.003
a = 300 m/s^{​​​​​​2}

Now given that,

 t = 0.01 sec

Using, v = u + at

0 = u - 300 x 0.01

u = 3 m/s

Again,
v² = u² + 2as
0 = 3^{​​​​​​2}  + 2 × (-300) × s
0 = 9 - 600s
s = 9/600
s = 0.015 m or 1.5 cm (option b) 
Regards