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Rotational Motion

269380 A stationary wheel starts rotating about its own axis at uniform angular acceleration $8 rad / s^{2}$ . The time taken by it to complete 77 rotations is

1

5.5 \sec

2

7 \sec

3

11 \sec

4

14 \sec

Explanation:

Given $ω_{i} = 0$ and $θ = \frac{1}{2} α t^{2}$

Rotational Motion

269381 A stationary wheel starts rotating about its own axis at constant angular acceleration. If the wheel completes 50 rotations in first 2 seconds, then the number of rotations made by it in next two seconds is

1 75

2 100

3 125

4 150

Explanation:

$ω_{i} = 0; t = 2 s$
$θ = 50 (2 π) = 100 π rad$
$∴ α = \frac{2 θ}{t^{2}} = \frac{200 π}{4} = 50 π rad s^{- 2}$
' $θ$ ' in $4 \sec; θ = \frac{1}{2} α t^{2} = \frac{1}{2} (50 π) (16)$ $= 400 π rad$
in the last $2 \sec, θ = 400 π - 100 π = 300 π rad$
$∴$ no.of rotations $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$

Rotational Motion

269382 If $\vec{F} = 2 \hat{i} - 3 \hat{j} N$ and $\vec{r} = 3 \hat{i} + 2 \hat{j}$ m then torque $\vec{τ}$ is

1

12 \hat{k}

2

13 \hat{k}

3

- 12 \hat{k}

4

- 13 \hat{k}

Explanation:

$\vec{τ} = \vec{r} \times \vec{F}$

Rotational Motion

269383 A crowbar of length $120 cm$ has its fulcrum situated at a distance of $20 cm$ from the load. The mechanical advantage of the crow bar is

1 1

2 3

3 5

4 7

Explanation:

$M A = \frac{effort arm}{load arm}$

Rotational Motion

269440 A circular disc is rotating about its own axis at a uniform angular velocity $ω$ . The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\frac{ω}{2}$ during 120 rotations. The number of rotations further made by it before coming to rest is

1 120

2 60

3 40

4 20

Explanation:

$α$ is constant, $α = \frac{ω_{1}^{2} - ω_{2}^{2}}{2 θ}; θ_{2} = \frac{θ_{1}}{3}$

Rotational Motion

269380 A stationary wheel starts rotating about its own axis at uniform angular acceleration $8 rad / s^{2}$ . The time taken by it to complete 77 rotations is

1

5.5 \sec

2

7 \sec

3

11 \sec

4

14 \sec

Explanation:

Given $ω_{i} = 0$ and $θ = \frac{1}{2} α t^{2}$

Rotational Motion

269381 A stationary wheel starts rotating about its own axis at constant angular acceleration. If the wheel completes 50 rotations in first 2 seconds, then the number of rotations made by it in next two seconds is

1 75

2 100

3 125

4 150

Explanation:

$ω_{i} = 0; t = 2 s$
$θ = 50 (2 π) = 100 π rad$
$∴ α = \frac{2 θ}{t^{2}} = \frac{200 π}{4} = 50 π rad s^{- 2}$
' $θ$ ' in $4 \sec; θ = \frac{1}{2} α t^{2} = \frac{1}{2} (50 π) (16)$ $= 400 π rad$
in the last $2 \sec, θ = 400 π - 100 π = 300 π rad$
$∴$ no.of rotations $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$

Rotational Motion

269382 If $\vec{F} = 2 \hat{i} - 3 \hat{j} N$ and $\vec{r} = 3 \hat{i} + 2 \hat{j}$ m then torque $\vec{τ}$ is

1

12 \hat{k}

2

13 \hat{k}

3

- 12 \hat{k}

4

- 13 \hat{k}

Explanation:

$\vec{τ} = \vec{r} \times \vec{F}$

Rotational Motion

269383 A crowbar of length $120 cm$ has its fulcrum situated at a distance of $20 cm$ from the load. The mechanical advantage of the crow bar is

1 1

2 3

3 5

4 7

Explanation:

$M A = \frac{effort arm}{load arm}$

Rotational Motion

269440 A circular disc is rotating about its own axis at a uniform angular velocity $ω$ . The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\frac{ω}{2}$ during 120 rotations. The number of rotations further made by it before coming to rest is

1 120

2 60

3 40

4 20

Explanation:

$α$ is constant, $α = \frac{ω_{1}^{2} - ω_{2}^{2}}{2 θ}; θ_{2} = \frac{θ_{1}}{3}$

Rotational Motion

269380 A stationary wheel starts rotating about its own axis at uniform angular acceleration $8 rad / s^{2}$ . The time taken by it to complete 77 rotations is

1

5.5 \sec

2

7 \sec

3

11 \sec

4

14 \sec

Explanation:

Given $ω_{i} = 0$ and $θ = \frac{1}{2} α t^{2}$

Rotational Motion

269381 A stationary wheel starts rotating about its own axis at constant angular acceleration. If the wheel completes 50 rotations in first 2 seconds, then the number of rotations made by it in next two seconds is

1 75

2 100

3 125

4 150

Explanation:

$ω_{i} = 0; t = 2 s$
$θ = 50 (2 π) = 100 π rad$
$∴ α = \frac{2 θ}{t^{2}} = \frac{200 π}{4} = 50 π rad s^{- 2}$
' $θ$ ' in $4 \sec; θ = \frac{1}{2} α t^{2} = \frac{1}{2} (50 π) (16)$ $= 400 π rad$
in the last $2 \sec, θ = 400 π - 100 π = 300 π rad$
$∴$ no.of rotations $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$

Rotational Motion

269382 If $\vec{F} = 2 \hat{i} - 3 \hat{j} N$ and $\vec{r} = 3 \hat{i} + 2 \hat{j}$ m then torque $\vec{τ}$ is

1

12 \hat{k}

2

13 \hat{k}

3

- 12 \hat{k}

4

- 13 \hat{k}

Explanation:

$\vec{τ} = \vec{r} \times \vec{F}$

Rotational Motion

269383 A crowbar of length $120 cm$ has its fulcrum situated at a distance of $20 cm$ from the load. The mechanical advantage of the crow bar is

1 1

2 3

3 5

4 7

Explanation:

$M A = \frac{effort arm}{load arm}$

Rotational Motion

269440 A circular disc is rotating about its own axis at a uniform angular velocity $ω$ . The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\frac{ω}{2}$ during 120 rotations. The number of rotations further made by it before coming to rest is

1 120

2 60

3 40

4 20

Explanation:

$α$ is constant, $α = \frac{ω_{1}^{2} - ω_{2}^{2}}{2 θ}; θ_{2} = \frac{θ_{1}}{3}$

Rotational Motion

269380 A stationary wheel starts rotating about its own axis at uniform angular acceleration $8 rad / s^{2}$ . The time taken by it to complete 77 rotations is

1

5.5 \sec

2

7 \sec

3

11 \sec

4

14 \sec

Explanation:

Given $ω_{i} = 0$ and $θ = \frac{1}{2} α t^{2}$

Rotational Motion

269381 A stationary wheel starts rotating about its own axis at constant angular acceleration. If the wheel completes 50 rotations in first 2 seconds, then the number of rotations made by it in next two seconds is

1 75

2 100

3 125

4 150

Explanation:

$ω_{i} = 0; t = 2 s$
$θ = 50 (2 π) = 100 π rad$
$∴ α = \frac{2 θ}{t^{2}} = \frac{200 π}{4} = 50 π rad s^{- 2}$
' $θ$ ' in $4 \sec; θ = \frac{1}{2} α t^{2} = \frac{1}{2} (50 π) (16)$ $= 400 π rad$
in the last $2 \sec, θ = 400 π - 100 π = 300 π rad$
$∴$ no.of rotations $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$

Rotational Motion

269382 If $\vec{F} = 2 \hat{i} - 3 \hat{j} N$ and $\vec{r} = 3 \hat{i} + 2 \hat{j}$ m then torque $\vec{τ}$ is

1

12 \hat{k}

2

13 \hat{k}

3

- 12 \hat{k}

4

- 13 \hat{k}

Explanation:

$\vec{τ} = \vec{r} \times \vec{F}$

Rotational Motion

269383 A crowbar of length $120 cm$ has its fulcrum situated at a distance of $20 cm$ from the load. The mechanical advantage of the crow bar is

1 1

2 3

3 5

4 7

Explanation:

$M A = \frac{effort arm}{load arm}$

Rotational Motion

269440 A circular disc is rotating about its own axis at a uniform angular velocity $ω$ . The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\frac{ω}{2}$ during 120 rotations. The number of rotations further made by it before coming to rest is

1 120

2 60

3 40

4 20

Explanation:

$α$ is constant, $α = \frac{ω_{1}^{2} - ω_{2}^{2}}{2 θ}; θ_{2} = \frac{θ_{1}}{3}$

Rotational Motion

269380 A stationary wheel starts rotating about its own axis at uniform angular acceleration $8 rad / s^{2}$ . The time taken by it to complete 77 rotations is

1

5.5 \sec

2

7 \sec

3

11 \sec

4

14 \sec

Explanation:

Given $ω_{i} = 0$ and $θ = \frac{1}{2} α t^{2}$

Rotational Motion

269381 A stationary wheel starts rotating about its own axis at constant angular acceleration. If the wheel completes 50 rotations in first 2 seconds, then the number of rotations made by it in next two seconds is

1 75

2 100

3 125

4 150

Explanation:

$ω_{i} = 0; t = 2 s$
$θ = 50 (2 π) = 100 π rad$
$∴ α = \frac{2 θ}{t^{2}} = \frac{200 π}{4} = 50 π rad s^{- 2}$
' $θ$ ' in $4 \sec; θ = \frac{1}{2} α t^{2} = \frac{1}{2} (50 π) (16)$ $= 400 π rad$
in the last $2 \sec, θ = 400 π - 100 π = 300 π rad$
$∴$ no.of rotations $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$

Rotational Motion

269382 If $\vec{F} = 2 \hat{i} - 3 \hat{j} N$ and $\vec{r} = 3 \hat{i} + 2 \hat{j}$ m then torque $\vec{τ}$ is

1

12 \hat{k}

2

13 \hat{k}

3

- 12 \hat{k}

4

- 13 \hat{k}

Explanation:

$\vec{τ} = \vec{r} \times \vec{F}$

Rotational Motion

269383 A crowbar of length $120 cm$ has its fulcrum situated at a distance of $20 cm$ from the load. The mechanical advantage of the crow bar is

1 1

2 3

3 5

4 7

Explanation:

$M A = \frac{effort arm}{load arm}$

Rotational Motion

269440 A circular disc is rotating about its own axis at a uniform angular velocity $ω$ . The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\frac{ω}{2}$ during 120 rotations. The number of rotations further made by it before coming to rest is

1 120

2 60

3 40

4 20

Explanation:

$α$ is constant, $α = \frac{ω_{1}^{2} - ω_{2}^{2}}{2 θ}; θ_{2} = \frac{θ_{1}}{3}$