A metre rod of mass 200 g is suspended by two strings at each end as shown in figure. A body of mass 300 g is suspended by a weightless string at 30 cm mark. The tensions in the string 2 is

Question

A metre rod of mass 200 g is suspended by two strings at each end as shown in figure. A body of mass 300 g is suspended by a weightless string at 30 cm mark. The tensions in the string 2 is (A) 6.6 N (B) 1.9 N (C) 1.3 N (D) 2 N

Tardigrade Admin · Accepted Answer

The various forces acting on the metre rod are shown in figure.
Net force acting on the rod is zero.
That is,

T_{1} + T_{2} - M g - m g = 0

or

T_{1} + T_{2} = (M + m) g

[

∴

g = 10 m

s^{- 1}

= (0.3 + 0.2)

\times

10 N = 0.5

\times

10 N = 5 N ....(1)

∴

Net torqure acting on the rod =

T_{2} \times (1.00 m) - M g \times (0.3 m) - m g \times (0.5 m)

For equilibrium, net torque acting on the body is zero

∴

T_{2} \times (1.00 m) - M g \times (0.5) - m g \times (0.5 m) = 0

i.e.

T_{2} = m g \times 0.5 + M g \times 0.3 = 0.2 \times 10 \times 0.5 + 0.3 \times 10 \times 0.3

= 1 + 0.9 = 1.9 N

Q. A metre rod of mass 200 g is suspended by two strings at each end as shown in figure. A body of mass 300 g is suspended by a weightless string at 30 cm mark. The tensions in the string 2 is

6.6 N

1.9 N

1.3 N

2 N