Rotational motion Quiz 1

Question 1

Four discs of radius $$R$$ are held at the vertices of a rectangle of dimension $$l 	imes b$$ in the figure. The moment of inertia around axis $$XX'$$ is described as $$ \ $$<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/396db831-7e1f-476f-bf86-1653578223668974547059547182934.png"/>

Accepted Answer

$$m{{R}^{2}}+2m{{b}^{2}}$$

Answer

$$2m{{R}^{2}}+2m{{b}^{2}}$$

Answer

$$\dfrac{m{{R}^{2}}}{4}+m{{b}^{2}}$$

Answer

$$2m{{R}^{2}}+\dfrac{m{{b}^{2}}}{2}$$

Question 2

A constant force acts in the line represented by $$y=4x-8$$ in $$3-D$$ space. If the magnitude of the force is $$5N$$, what would be the resultant torque due to this force about the origin.

Accepted Answer

$$\dfrac{40}{\sqrt{82}}$$

Answer

$$\dfrac{40}{\sqrt{41}}$$

Answer

$$\dfrac{64}{\sqrt{82}}$$

Answer

$$\dfrac{64}{\sqrt{41}}$$

Question 3

A massless charge $$Q$$ is added to a solid sphere of radius $$R$$ and mass $$M$$ and connected to the end of a massless rod of length $$\ell $$. The opposite end of the rod is set at $$O$$ and serves as a pivot. The figure depicts the setup of a uniform electric field $$E$$. When the electric field is turned on, calculate the instantaneous angular acceleration. $$ \ $$<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/9965e01c-a10a-4f3f-aa16-4e50a071f76b1038387446581217572.png"/>

Accepted Answer

$$\dfrac{QE\left( R+\ell  \right)}{M\left( \dfrac{7}{5}{{R}^{2}}+{{\ell }^{2}}+2R\ell  \right)}$$

Answer

$$\dfrac{QER}{M\left( \dfrac{7}{5}{{R}^{2}}+{{\ell }^{2}} \right)}$$

Answer

$$\dfrac{QE\ell }{M\left( {{R}^{2}}+{{\ell }^{2}} \right)}$$

Answer

$$\dfrac{QE\left( R+\ell  \right)}{M\left( \dfrac{2}{5}{{R}^{2}}+{{\ell }^{2}}+2R\ell  \right)}$$

Question 4

If a disc with mass $$\left( m ight)$$ is allowed to fall down the plane as shown in the figure, and friction is sufficient to prevent slipping, then the time taken by the disc to reach the bottom is $$ \ $$<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/8d572421-5a50-4f2e-bda3-274acd980e584248565033408812868.png"/>

Accepted Answer

$$2{{\left( \dfrac{3h}{g} \right)}^{\dfrac{1}{2}}}$$

Answer

$$2\sqrt{\dfrac{6h}{g}}$$

Answer

$$\dfrac{\sqrt{3}}{2}	imes {{\left( \dfrac{3h}{2} ight)}^{\dfrac{1}{2}}}$$

Answer

$$\dfrac{2}{\sqrt{3}}	imes {{\left( \dfrac{3h}{2} ight)}^{\dfrac{1}{2}}}$$

Question 5

Calculate the moment of Inertia about an axis perpendicularly passing to the plane of the plate through centre $$O$$.<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/ad395d9f-c3ea-4312-8e42-ed722e823be28438982982177723870.png"/>

Accepted Answer

$$\rho {{a}^{4}}\left( \dfrac{128}{3}-\dfrac{3}{2}\pi  \right)$$

Answer

$$\rho {{a}^{4}}\left( \dfrac{8}{3}-\dfrac{\pi }{2} \right)$$

Answer

$$\rho {{a}^{4}}\left( \dfrac{128}{3}-\dfrac{\pi }{2} \right)$$

Answer

$$\rho {{a}^{4}}\left( \dfrac{8}{3}-\dfrac{3\pi }{2} \right)$$