Question

Question 5.15 Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?

Chapter Laws Of Motion Page 110

Answer 1

Given,
Mass of body (m1) = 10 Kg
Mass of body (m2) = 20 Kg
Horizontal force F = 600 N
Let a is the acceleration of system

(A) when force F applied on A:
use free body diagram ,
For body m1 ,
F - T = m1a ______________(1)
For body m2 ,
T = m2a ___________(2)
Solve eqns (1) and (2)
a = F/(m1 + m2)
= 600/(10 + 20)
= 20 m/s²
And T = m2a = 20×20 = 400 N

(B) again, using free body diagram when force on B
For body m1 ,
T = m1a _____________(1)
For body B,
F - T = m2a ___________(2)
Solve eqns (1) and (2)
a = F/(m1 + m2)
= 600/(10+20)
= 30 m/s²
And T = 10×20 = 200 N

Answer 2

the direction of string. What is the tension in the string in each case is 200 N