A body of mass 20 ~kg is moving on a rough horizontal plane. A block of mass 3 ~kg is connected to the 20 ~kg mass by a string of negligible mass through a smooth pulley as shown in the below figure. The tension in the string is 27 ~N . The coefficient of kinetic friction between the heavier mass and the swrface is (g=10 ~m / s ^2 . )

Step-by-step solution

Given, tension in string (T)=27 ~N Mass (m)=3 ~kg Let acceleration of the block be a . array rlrl & & 3 g-T & =m a & & 10 3-27 & =3 a & & 30-27 & =3 a & a & = 3 3 =1 ~m / s ^2 array For the body, we have, aligned & & 27- 20 g & =20 a & & 27- 20 10 & =20 1 & & 27-200 & =20 & & 200 & =27-20 aligned Coefficient of kinetic friction, = 7 200 =0.035 Coefficient of kinetic friction is 0.035