SATHEE: Rotation 3 Question 10

Rotation 3 Question 10

16. The maximum value of $v_{0}$ for which the disk will roll without slipping is

(a) $μ g \sqrt{\frac{M}{k}}$

(b) $μ g \sqrt{\frac{M}{2 k}}$

(d) $μ g \sqrt{\frac{5 M}{2 k}}$

Objective Questions II (One or more correct option)

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Answer:

Correct Answer: 16. (c)

Solution:

In case of pure rolling, mechanical energy will remain conserved.

$\begin{aligned} ∴ \frac{1}{2} M v_{0}^{2} + \frac{1}{2} \frac{1}{2} M R^{2} & \frac{v_{0}}{R} & = 2 \frac{1}{2} k x^{2}_{max}^{2} \\ ∴ x_{max} & = \sqrt{\frac{3 M}{4 k}} v_{0} \\ As, & = \frac{2 k x}{3} \\ ∴ F_{max} = μ M g = \frac{2 k x_{max}}{3} & = \frac{2 k}{3} \sqrt{\frac{3 M}{4 k}} v_{0} \\ ∴ v_{0} & = μ g \sqrt{\frac{3 M}{k}} \end{aligned}$

Rotation 3 Question 10

16. The maximum value of $v_{0}$ for which the disk will roll without slipping is

Answer:

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Rotation 3 Question 10

16. The maximum value of v0 for which the disk will roll without slipping is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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16. The maximum value of $v_{0}$ for which the disk will roll without slipping is