A mass of 0.1 kg is hung at the 20 cm mark from a 1 m rod weighing 0.25 kg pivoted at its centre. The rod will not topple if

Question

A mass of 0.1 kg is hung at the 20 cm mark from a 1 m rod weighing 0.25 kg pivoted at its centre. The rod will not topple if (A) No other mass is attached to the rod (B) 0.15 kg is hung at 80 cm mark (C) 0.15 kg is hung at 70 cm mark (D) 0.10 kg is hung at 70 cm mark

Tardigrade Admin · Accepted Answer

Given situation is shown in the figure.
Here,

m_{1} = 0.1 k g,

x = 50 - 20 = 30 cm = 0.3 m
Apply law of moments about centre of the rod,

m_{1} gx = m_{2} g x^{'}

m_{2} x^{'} = 0.1 \times 0.3 = 0.03 k g m

Hence according to options

m_{2} = 0.15 k g, x^{'} = 0.2 m = 20 c m

Hence rod will not topple if second mass of
0.15 kg is hung at 70 cm mark.

Q. A mass of 0.1 kg is hung at the 20 cm mark from a 1 m rod weighing 0.25 kg pivoted at its centre. The rod will not topple if

No other mass is attached to the rod

0.15 kg is hung at 80 cm mark

0.15 kg is hung at 70 cm mark

0.10 kg is hung at 70 cm mark