Question

Three small balls each of mass 100 gm are attached at distance of 1 m, 2 m and 3 m from end D of a 3 m length
string. The string is rotated with uniform angular velocity in a horizontal plane about D. If the outside ball is moving
a speed of 6 m/s, the ratio of tension in the three parts of the string from inside-
(1) 6:5:4
(2) 3:2:1
(3) 3:5:6
(4) 6:5:3​

Answer 1

Thus the ratio of tension in the three parts of the string from inside is 6 : 5 : 3

Option (4) is correct.

Explanation:

We know that

T3 = mv^2 / r

T3 =  mv^2 / r = mω^2 r

T3 = 0.1  6^2 / 3 = 1.2 N

T2 = 0.1 x 2^2 x 2 + 1.2 = 2 N

T1 = 2 + 0.1 x 2^2 x 1

T1 = 2 + 0.4 = 2.4 N

T1 : T2 : T3

2.4 : 2 : 1.2

Now multiply with 2.5 to convert the ratio into whole number.

2.4 x 2.5 : 2 x 2.5 : 2.5 x 1.2

6 : 5 : 3

Thus the ratio of tension in the three parts of the string from inside is 6 : 5 : 3