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