Q128 / 160 · TS EAMCET 2024 (09 May Shift 1) · Physics

A solid sphere rolls down without slipping from the top of an inclined plane of height 28 m and angle of inclination $30^{\circ}$. The velocity of the sphere, when it reaches the bottom of the plane is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

  • Correct answer
    A
    $20 \mathrm{~ms}^{-1}$
  • B
    $28 \mathrm{~ms}^{-1}$
  • C
    $10 \mathrm{~ms}^{-1}$
  • D
    $14 \mathrm{~ms}^{-1}$

Solution

Velocity of sphere rolls down without slipping $v=\sqrt{\frac{2 \mathrm{gh}}{1+\frac{\mathrm{k}^2}{\mathrm{R}^2}}}=\sqrt{\frac{2 \times 10 \times 28}{1+\frac{2}{5}}}=\sqrt{\frac{2 \times 10 \times 28 \times 5}{7}}=20 \mathrm{~m} / \mathrm{s}$

Hence, the correct answer is option: 'A'.

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