A solid cylinder of mass m and radius r rolls on fixed cylindrical surface of radius R at the instant shown line joining both the centre is rotating with angular velocity $ω$ and angular acceleration $α$ . Find the acceleration point P which is the point of the rolling cylinder in contact with the fixed cylinder.

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$ω^{2} \frac{(R - r) R}{r}$

$ω^{2} \frac{r^{2}}{R}$

$ω^{2} \frac{R^{2}}{r}$

$ω^{2} \frac{(R + r) R}{r}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$a_{c o m} = ω^{2} (R + r)$

$ω (R + r) = ω' r$

$ω' = \frac{ω (R + r)}{r}$

$a_{p c o m} = ω^{12} r$ $= \frac{ω^{2} {(R + r)}^{2}}{r}$

$a_{p} = \frac{ω^{2} {(R + r)}^{2}}{r} - ω^{2} (R + r)$ $= ω^{2} (R + r) (\frac{R + r}{r} - 1)$

$a_{p} = \frac{ω^{2} (R + r) R}{r}$

Watch 3-min video & get full concept clarity