Rolling motion

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Question

A solid disc of radius ‘a’ and mass ‘m’ rolls down without slipping on an inclined plane making an angle $θ$ with the horizontal. The acceleration of the disc will be $\frac{2}{b} g sin θ$ where b is ______(Round off to the Nearest Integer)
(g=acceleration due to gravity $θ$ =angle as shown in figure)

Moderate

Solution

$\begin{array}{l} T r a n s l a t i o n, m g \sin θ - f = m a_{c m} \\ R o t a t i o n, f . a = \frac{m a^{2}}{2} \cdot α \\ P u r e R o l l i n g, a_{c m} = α a \\ On solving \\ a_{c m} = \frac{2}{3} g \sin θ \\ \Rightarrow b = 3 \end{array}$

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Rolling motion

Remember concepts with our Masterclasses.

A solid disc of radius ‘a’ and mass ‘m’ rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be 2b g sinθ where b is ______(Round off to the Nearest Integer)(g=acceleration due to gravity θ=angle as shown in figure)

Translation , mgsin⁡θ−f=macmRotation , f.a=ma22⋅αPure Rolling , acm=αa On solving acm=23gsin⁡θ ⇒b=3

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$\begin{array}{l} T r a n s l a t i o n, m g \sin θ - f = m a_{c m} \\ R o t a t i o n, f . a = \frac{m a^{2}}{2} \cdot α \\ P u r e R o l l i n g, a_{c m} = α a \\ On solving \\ a_{c m} = \frac{2}{3} g \sin θ \\ \Rightarrow b = 3 \end{array}$