A rod of mass 'M' and length '2L' is suspended at its middle by a… | JEE Main 2019 (9 Jan, Shift 2)

Q16JEE Main 2019 · 9 JAN · SHIFT 2Difficult

Other SHM Systems

A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to:

Show answer and solution

Answer: (c)

Torsional pendulum: $f \propto \frac{1}{\sqrt{I}}$ . $I_0 = \frac{M(2L)^2}{12} = \frac{ML^2}{3}$ .
With the masses: $I_1 = \frac{ML^2}{3} + 2m\left(\frac{L}{2}\right)^2 = \frac{ML^2}{3} + \frac{mL^2}{2}$ .
$f_1 = 0.8f_0 \Rightarrow \frac{I_1}{I_0} = \frac{1}{0.64} = 1.5625$
$\frac{3m}{2M} = 0.5625 \Rightarrow \frac{m}{M} = 0.375 \approx 0.37$ , answer (c).

Report a mistake

More questions on Other SHM Systems

A cylindrical block of wood (density = 650 kg m ⁻³), of base area 30 cm2 and height 54…JEE Main 2015 (11 Apr, Shift 1)
A pendulum made of a uniform wire of cross sectional area A has time period T. When an…JEE Main 2015
A uniform cylinder of length L and mass M having cross-sectional area A is suspended…JEE Main 2013 (25 Apr, Shift 1)
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston…JEE Main 2013
A rectangular block of mass m and area of cross-section A floats in a liquid of density…NEET 2006 (AIPMT)
A cylindrical block of mass M and area of cross section A is floating in a liquid of…JEE Main 2026 (24 Jan, Shift 1)
A small sphere oscillates simple harmonically in a watch glass whose radius of curvature…MHT CET 2026 (15 Apr, Shift 1)
A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in…JEE Main 2026 (4 Apr, Shift 2)

Other SHM Systems question from JEE Main 2019 (9 Jan, Shift 2)

More questions on Other SHM Systems