Physics, asked by thegreatdude, 8 months ago

1.
(i) If two circular discs A and B of masses m, 3 m and radii R, 2R, respectively, are released
from the top of a rough inclined plane, which disc will reach the bottom first.
(ii) If a solid sphere and a hollow sphere are released from the top of a rough inclined plane,
which sphere will reach the bottom first.​

Answers

Answered by Ekaro
22

★ Time taken by object (ring / disc / solid sphere / hollow sphere) to reach the bottom can be calculated by using this formula :

\dag\:\:\boxed{\bf{\blue{t=\sqrt{\dfrac{2h{\large(}1 +  \dfrac{ {k}^{2} }{ {r}^{2} }{\large)}}{g\sin^2\theta} }}}}

Answer - 1 :

For disc A :

➠ I₁ = M₁R₁²/2

➠ mk² = mR²/2

k²/R² = 1/2

For disc B :

➠ I₂ = M₂R₂²/2

➠ (3m)k² = (3m)(2R)²/2

➠ k² = 4R²/2

k²/R² = 2

★ According to formula of time, we can say that time required to reach the bottom is directly proportional to the square root of (1+k²/R²). Moreover value of k²/R² for disc B is greater than disc A.

Disc A will reach the bottom first.

Answer - 2 :

For hollow sphere :

➠ MK² = 2/3 MR²

k²/R² = 2/3

For solid sphere :

➠ Mk² = 2/5 MR²

k²/R² = 2/5

Here value of k²/R² for hollow sphere is greater than solid sphere.

Solid sphere will reach the bottom first.

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