Question types

Rotational Dynamics question types

383 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

383
Questions
5
Question groups
5
Question types
Sample Questions

Rotational Dynamics questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

The centripetal acceleration of the bob of a conical pendulum is
  • A
    $\frac{r g}{\cos \theta}$
  • B
    $\frac{r g}{L}$
  • C
    $\frac{g}{L}$
  • $\frac{r g}{L \cos \theta}$.

Answer: D.

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A conical pendulum of string length $L$ and bob of mass $m$ performs UCM along a circular path of radius $r$. The tension in the string is
  • $\frac{m g L}{\sqrt{L^2-r^2}}$
  • B
    $\frac{m g L}{\sqrt{L^2+r^2}}$
  • C
    $\frac{m g L}{\sqrt{2} r}$
  • D
    $\frac{m r g \tan \theta}{L}$

Answer: A.

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The period of a conical pendulum in terms of its length $(I)$, semivertical angle $(\theta)$ and acceleration due to gravity $(\mathrm{g})$, is
  • A
    $\frac{1}{2 \pi} \sqrt{\frac{l \cos \theta}{g}}$
  • B
    $\frac{1}{2 \pi} \sqrt{\frac{l \sin \theta}{g}}$
  • $4 \pi \sqrt{\frac{l \cos \theta}{4 g}}$
  • D
    $4 \pi \sqrt{\frac{l \tan \theta}{g}}$.

Answer: C.

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A track for a certain motor sport event is in the form of a circle and banked at an angle 6 . For a car driven in a circle of radius $r$ along the track at the optimum speed, the periodic time is
  • A
    $\sqrt{\frac{r}{g}}$
  • B
    $2 \pi \sqrt{\frac{r}{g}}$
  • $2 \pi \sqrt{\frac{r}{g \tan \theta}}$
  • D
    $2 \pi \sqrt{\frac{r \tan \theta}{g}}$.

Answer: C.

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The maximum speed with which a car can be driven safely along a curved road of radius $17.32 \mathrm{~m}$ and banked at $30^{\circ}$ with the horizontal is $\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right.$ ]
  • A
    $5 \mathrm{~m} / \mathrm{s}$
  • $10 \mathrm{~m} / \mathrm{s}$
  • C
    $15 \mathrm{~m} / \mathrm{s}$
  • D
    $20 \mathrm{~m} / \mathrm{s}$.

Answer: B.

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Calculate the $\mathrm{Ml}$ and rotational kinetic energy of a thin uniform rod of mass $10 \mathrm{~g}$ and length $60 \mathrm{~cm}$ when it rotates about a transverse axis through its centre at $90 \mathrm{rpm}$.
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A solid cylinder of uniform density and radius $2 \mathrm{~cm}$ has a mass of $50 \mathrm{~g}$. If its length is $12 \mathrm{~cm}$, calculate its moment of inertia about an axis passing through its centre and perpendicular to its length.
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A thin rod of uniform cross section is made up of two sections made of wood and steel. The wooden section has length $50 \mathrm{~cm}$ and mass $0.6 \mathrm{~kg}$. The steel section has length $30 \mathrm{~cm}$ and mass $3 \mathrm{~kg}$. Find the moment of inertia of the rod about a transverse axis passing through the junction of the two sections.
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A thin rod of uniform cross section is made up of two sections made of wood and steel. The wooden section has length $50 \mathrm{~cm}$ and mass $0.6 \mathrm{~kg}$. The steel section has length $30 \mathrm{~cm}$ and mass $3 \mathrm{~kg}$. Find the moment of inertia of the rod about a transverse axis passing through the junction of the two sections.
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