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

(B) Let the centre of the bigger disc of radius $2R$ be at the origin $(0,0)$.Let $M$ be the mass of the bigger disc. The mass per unit area is $\sigm

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(B) Let the centre of the bigger disc of radius $2R$ be at the origin $(0,0)$.Let $M$ be the mass of the bigger disc. The mass per unit area is $\sigma = \frac{M}{\pi(2R)^2} = \frac{M}{4\pi R^2}$.The mass of the removed smaller disc of radius $R$ is $m = \sigma \cdot \pi R^2 = \frac{M}{4\pi R^2} \cdot \pi R^2 = \frac{M}{4}$.The centre of mass of the bigger disc is at $x_1 = 0$. The centre of mass of the removed smaller disc is at $x_2 = R$ (since the circumferences touch).The centre of mass of the remaining part is given by:$x_{CM} = \frac{M x_1 - m x_2}{M - m}$$x_{CM} = \frac{M(0) - (M/4)(R)}{M - M/4} = \frac{-MR/4}{3M/4} = -\frac{R}{3}$.The distance from the centre of the bigger disc is $|x_{CM}| = \frac{R}{3}$.Comparing this with $\alpha R$,we get $\alpha = \frac{1}{3}$.

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

Similar Questions

Which part of the body secretes the hormone secretin?

If $x > 0, y > 0, z > 0, xy + yz + zx < 1$ and if $\tan^{-1} x + \tan^{-1} y + \tan^{-1} z = \pi$,then $x + y + z$ equals to

If $|a| < 1$ and $b = \sum_{k=1}^{\infty} \frac{a^k}{k}$,then $a$ is equal to

For the combination of logic gates shown in the figure,the equivalent logic gate is

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module