A circular disc of radius R is removed from a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $\sigma$ be the surface mass density of the discs.Mass of the bigger disc $M = \sigma \pi (2R)^2 = 4 \sigma \pi R^2$.Mass of the removed small

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(A) Let $\sigma$ be the surface mass density of the discs.Mass of the bigger disc $M = \sigma \pi (2R)^2 = 4 \sigma \pi R^2$.Mass of the removed smaller disc $m = \sigma \pi R^2$.Let the origin be at the centre of the bigger disc. The centre of the removed disc is at a distance $d = R$ from the origin.The centre of mass of the remaining part is given by $X_{cm} = \frac{M(0) - m(d)}{M - m}$.$X_{cm} = \frac{0 - (\sigma \pi R^2)(R)}{4 \sigma \pi R^2 - \sigma \pi R^2} = \frac{-\sigma \pi R^3}{3 \sigma \pi R^2} = -\frac{R}{3}$.The magnitude of the distance is $\frac{R}{3}$,so $\alpha R = \frac{R}{3}$,which gives $\alpha = \frac{1}{3}$.

$A$ circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

Similar Questions

What is responsible for the resistance of insects to insecticides?

A prism of angle $75^\circ$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index $1.5$ only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be . . . . . . .
$(\sin 15^\circ = 0.25$ and $\sin 25^\circ = 0.43)$

If $P$ is a point such that the ratio of the square of the lengths of the tangents from $P$ to the circles $x^2+y^2+2x-4y-20=0$ and $x^2+y^2-4x+2y-44=0$ is $2:3$,then the locus of $P$ is a circle with centre :

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is

The statement $\sim (p \leftrightarrow \sim q)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module