A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is __________ J.

$(g = 10 {m/s}^{2})$ [2026]

Question

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is __________ J.

$(g = 10 {m/s}^{2})$ [2026]

Smart Achievers · Accepted Answer

(30)

$m g \times 3 = \frac{1}{2} \cdot \frac{m R^{2}}{2} \cdot ω^{2} + \frac{1}{2} m v^{2} . . . (i)$

$& v = ω R . . . (i i)$

$From equation (i) & (ii)$

$g \times 3 = \frac{3}{4} v^{2}$

$K.E. of flywheel = \frac{1}{2} \times \frac{m R^{2}}{2} \times ω^{2} = \frac{1}{4} m v^{2}$

$= \frac{1}{4} \times 3 \times 40 = 30 Joule$

Solution

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Solution

Ans. (30) mg×3=12·mR22·ω2+12mv2 ...(i) & v=ωR ...(ii) From equation (i) & (ii) g×3=34v2 K.E. of flywheel=12×mR22×ω2=14mv2 =14×3×40=30 Joule

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