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Rotational Motion

269611 A square is made by joining four rods each of mass $M$ and length $L$ . Its moment of inertia about an axis PQ, in its plane and passing through one of its corner is

1

6 M L^{2}

2

\frac{4}{3} M L^{2}

3

\frac{8}{3} M L^{2}

4

\frac{10}{3} M L^{2} +

Explanation:

M.I about an axis passing through the diagonal $I_{g} = \frac{2 M L^{2}}{3}$ M.I about the given axis ${I = I_{g} + 4 M \frac{L}{[\sqrt{2}}]}^{i}$

Rotational Motion

269612 A shaft is turning at $65 rad / \sec$ at time zero. Thereafter, angular acceleration is given by $α = (- 10 - 5 t) rad / s^{2}$ where $t$ is the elapsed time. Find its angular speed at $t = 3$ sec.

1

25 rad / \sec

2

12.5 rad / \sec

3

17 rad / \sec

4

22 rad / \sec

Explanation:

$ω = \int α d t$

Rotational Motion

269613 A wheel having radius $10 cm$ is coupled by a belt to another wheel of radius $30 cm$ . $1 st$ wheel increases its angular speed from rest at a uniform rate of $1.57 rad s^{- 2}$ . The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

1

20 \sec

2

10 \sec

3

1.5 \sec

4

15 \sec

Explanation:

At any instant linear acceleration of all points of coupled belt is same. $a = r α$
$r_{1} α_{1} = r_{2} α_{2};$ find $α_{2}; ω_{2} = ω_{1} + α_{2} t$ $t = \frac{ω_{2}}{α_{2}} ∵ ω_{1} = 0$

Rotational Motion

269614 An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $μ$ . A horizontal force $F$ is applied on the prism as shown. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, the minimum force required to topple the prism is

1

\frac{m g}{\sqrt{3}}

2

\frac{m g}{4}

3

\frac{μ m g}{\sqrt{3}}

4

\frac{μ m g}{4}

Explanation:

About right base corner $; τ_{F} = τ_{m g}$

Rotational Motion

269611 A square is made by joining four rods each of mass $M$ and length $L$ . Its moment of inertia about an axis PQ, in its plane and passing through one of its corner is

1

6 M L^{2}

2

\frac{4}{3} M L^{2}

3

\frac{8}{3} M L^{2}

4

\frac{10}{3} M L^{2} +

Explanation:

M.I about an axis passing through the diagonal $I_{g} = \frac{2 M L^{2}}{3}$ M.I about the given axis ${I = I_{g} + 4 M \frac{L}{[\sqrt{2}}]}^{i}$

Rotational Motion

269612 A shaft is turning at $65 rad / \sec$ at time zero. Thereafter, angular acceleration is given by $α = (- 10 - 5 t) rad / s^{2}$ where $t$ is the elapsed time. Find its angular speed at $t = 3$ sec.

1

25 rad / \sec

2

12.5 rad / \sec

3

17 rad / \sec

4

22 rad / \sec

Explanation:

$ω = \int α d t$

Rotational Motion

269613 A wheel having radius $10 cm$ is coupled by a belt to another wheel of radius $30 cm$ . $1 st$ wheel increases its angular speed from rest at a uniform rate of $1.57 rad s^{- 2}$ . The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

1

20 \sec

2

10 \sec

3

1.5 \sec

4

15 \sec

Explanation:

At any instant linear acceleration of all points of coupled belt is same. $a = r α$
$r_{1} α_{1} = r_{2} α_{2};$ find $α_{2}; ω_{2} = ω_{1} + α_{2} t$ $t = \frac{ω_{2}}{α_{2}} ∵ ω_{1} = 0$

Rotational Motion

269614 An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $μ$ . A horizontal force $F$ is applied on the prism as shown. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, the minimum force required to topple the prism is

1

\frac{m g}{\sqrt{3}}

2

\frac{m g}{4}

3

\frac{μ m g}{\sqrt{3}}

4

\frac{μ m g}{4}

Explanation:

About right base corner $; τ_{F} = τ_{m g}$

Rotational Motion

269611 A square is made by joining four rods each of mass $M$ and length $L$ . Its moment of inertia about an axis PQ, in its plane and passing through one of its corner is

1

6 M L^{2}

2

\frac{4}{3} M L^{2}

3

\frac{8}{3} M L^{2}

4

\frac{10}{3} M L^{2} +

Explanation:

M.I about an axis passing through the diagonal $I_{g} = \frac{2 M L^{2}}{3}$ M.I about the given axis ${I = I_{g} + 4 M \frac{L}{[\sqrt{2}}]}^{i}$

Rotational Motion

269612 A shaft is turning at $65 rad / \sec$ at time zero. Thereafter, angular acceleration is given by $α = (- 10 - 5 t) rad / s^{2}$ where $t$ is the elapsed time. Find its angular speed at $t = 3$ sec.

1

25 rad / \sec

2

12.5 rad / \sec

3

17 rad / \sec

4

22 rad / \sec

Explanation:

$ω = \int α d t$

Rotational Motion

269613 A wheel having radius $10 cm$ is coupled by a belt to another wheel of radius $30 cm$ . $1 st$ wheel increases its angular speed from rest at a uniform rate of $1.57 rad s^{- 2}$ . The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

1

20 \sec

2

10 \sec

3

1.5 \sec

4

15 \sec

Explanation:

At any instant linear acceleration of all points of coupled belt is same. $a = r α$
$r_{1} α_{1} = r_{2} α_{2};$ find $α_{2}; ω_{2} = ω_{1} + α_{2} t$ $t = \frac{ω_{2}}{α_{2}} ∵ ω_{1} = 0$

Rotational Motion

269614 An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $μ$ . A horizontal force $F$ is applied on the prism as shown. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, the minimum force required to topple the prism is

1

\frac{m g}{\sqrt{3}}

2

\frac{m g}{4}

3

\frac{μ m g}{\sqrt{3}}

4

\frac{μ m g}{4}

Explanation:

About right base corner $; τ_{F} = τ_{m g}$

Rotational Motion

269611 A square is made by joining four rods each of mass $M$ and length $L$ . Its moment of inertia about an axis PQ, in its plane and passing through one of its corner is

1

6 M L^{2}

2

\frac{4}{3} M L^{2}

3

\frac{8}{3} M L^{2}

4

\frac{10}{3} M L^{2} +

Explanation:

M.I about an axis passing through the diagonal $I_{g} = \frac{2 M L^{2}}{3}$ M.I about the given axis ${I = I_{g} + 4 M \frac{L}{[\sqrt{2}}]}^{i}$

Rotational Motion

269612 A shaft is turning at $65 rad / \sec$ at time zero. Thereafter, angular acceleration is given by $α = (- 10 - 5 t) rad / s^{2}$ where $t$ is the elapsed time. Find its angular speed at $t = 3$ sec.

1

25 rad / \sec

2

12.5 rad / \sec

3

17 rad / \sec

4

22 rad / \sec

Explanation:

$ω = \int α d t$

Rotational Motion

269613 A wheel having radius $10 cm$ is coupled by a belt to another wheel of radius $30 cm$ . $1 st$ wheel increases its angular speed from rest at a uniform rate of $1.57 rad s^{- 2}$ . The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

1

20 \sec

2

10 \sec

3

1.5 \sec

4

15 \sec

Explanation:

At any instant linear acceleration of all points of coupled belt is same. $a = r α$
$r_{1} α_{1} = r_{2} α_{2};$ find $α_{2}; ω_{2} = ω_{1} + α_{2} t$ $t = \frac{ω_{2}}{α_{2}} ∵ ω_{1} = 0$

Rotational Motion

269614 An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $μ$ . A horizontal force $F$ is applied on the prism as shown. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, the minimum force required to topple the prism is

1

\frac{m g}{\sqrt{3}}

2

\frac{m g}{4}

3

\frac{μ m g}{\sqrt{3}}

4

\frac{μ m g}{4}

Explanation:

About right base corner $; τ_{F} = τ_{m g}$

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