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  4. A uniform disc with mass M=4 kg and radius R= 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m =2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is N. (Take g =10 ms -2 )

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Q. A uniform disc with mass $M=4 \,kg$ and radius $R= 10 \,cm$ is mounted on a fixed horizontal axle as shown in figure. A block with mass $m =2 \,kg$ hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____$N$. (Take $g =10 \,ms ^{-2}$ )Physics Question Image

JEE MainJEE Main 2022System of Particles and Rotational Motion

Solution:

image
$2 g-T=2 a ....$(1)
$TR =\frac{ MR ^{2}}{2} \alpha ....$(2)
$\alpha=\frac{ a }{ R } ....$(3)
$T =2 a$
$2 g - T =2 a$
$T = g =10 \,N$