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 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
Updated On: May 12, 2024
- 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
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The Correct Option is C
Solution and Explanation
Given situation is shown in the figure.
Here, $m_1 = 0.1 \, kg,$
x = 50 - 20 = 30 cm = 0.3 m
Apply law of moments about centre of the rod,
$m_1 gx = m_2 gx'$
$m_2x' = 0.1 \times 0.3 = 0.03 \, kg\, m$
Hence according to options
$m_2 = 0.15\, kg, x' = 0.2\, m = 20 \, cm$
Hence rod will not topple if second mass of
0.15 kg is hung at 70 cm mark.
Here, $m_1 = 0.1 \, kg,$
x = 50 - 20 = 30 cm = 0.3 m
Apply law of moments about centre of the rod,
$m_1 gx = m_2 gx'$
$m_2x' = 0.1 \times 0.3 = 0.03 \, kg\, m$
Hence according to options
$m_2 = 0.15\, kg, x' = 0.2\, m = 20 \, cm$
Hence rod will not topple if second mass of
0.15 kg is hung at 70 cm mark.
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.