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 be the origin $O(0,0)$.Let the mass of the original disc be $M$ and its radius be $2R$.The mass of the removed s

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(B) Let the centre of the bigger disc be the origin $O(0,0)$.Let the mass of the original disc be $M$ and its radius be $2R$.The mass of the removed smaller disc of radius $R$ is $m = \frac{\pi R^2}{\pi (2R)^2} M = \frac{M}{4}$.The centre of the removed disc is at a distance $R$ from the origin along the $x$-axis,so its coordinates are $(R, 0)$.The centre of mass of the remaining part $(x_{CM})$ is given by the formula:$x_{CM} = \frac{M_1 x_1 - m x_2}{M_1 - m}$Here,$M_1 = M$,$x_1 = 0$,$m = M/4$,and $x_2 = R$.$x_{CM} = \frac{M(0) - (M/4)(R)}{M - M/4} = \frac{-MR/4}{3M/4} = -\frac{R}{3}$.The distance from the centre 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

When a resistor of $11 \Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \ A$. Instead,when a resistor of $5 \Omega$ is connected to the same electric cell in series,the current increases by $0.4 \ A$. The internal resistance of the cell is (in $\Omega$)

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ is:

If $f(1)=1$ and $f^{\prime}(1)=3$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has a moment of inertia $I$ about an axis passing through its center and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of this sphere about its diameter is:

The chemicals and the reaction conditions required for the preparation of ethane are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module