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PHXI06:WORK ENERGY AND POWER

355706 A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1 The mass is at the highest point

2 The wire is horizontal

3 The mass is at the lowest point

4 Inclined at an angle of

60^{\circ}

from vertical

NEET - 2019

PHXI06:WORK ENERGY AND POWER

355707 A bob of mass ' $m$ ' is suspended by a light string of length ' $L$ '. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$ . The ratio of kinetic energies $\frac{{(K . E .)}_{A}}{{(K . E .)}_{B}}$ is
supporting img

1

3 : 2

2

1 : 5

3

2 : 5

4

5 : 1

Explanation:

The critical velocity at $A$ is $v_{L} = \sqrt{5 g L}$ and at $B$ is $v_{H} = \sqrt{g L}$ .
$K E_{A} = \frac{1}{2} m v_{L}^{2} K E_{B} = \frac{1}{2} m v_{H}^{2}$
supporting img

So, $\frac{K E_{A}}{K E_{B}} = \frac{v_{L}^{2}}{v_{H}^{2}} = \frac{5 g L}{g L} = \frac{5}{1}$

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355708 With what minimum speed $v$ must a small ball should be pushed inside a smooth vertical tube from a height $h$ so that it may reach the top of the tube? Radius of the tube is $R$ .

1

\sqrt{g (5 R - 2 h)}

2

\sqrt{2 g (h + 2 R)}

3

\sqrt{2 g (2 R - h)}

4

\frac{5}{2} R

Explanation:

Velocity of a ball to just reach the top of the tube should be given by;
$0 = v^{2} - 2 g h_{0}$
Where the velocity will be zero at topmost point.
Here $h_{0} = (2 R - h)$
Thus $v = \sqrt{2 g (2 R - h)}$

PHXI06:WORK ENERGY AND POWER

355709 An insect jumps from ball $A$ onto ball $B$ . which are suspended from inextensible light strings each of length $L = 8 c m$ . The mass of each ball and insect is same. What should be the minimum relative velocity of jump of insect w.r.t. ball $A$ , if both the balls manage to complete the full circle?
supporting img

1

8 m s^{- 1}

2

4 m s^{- 1}

3

12 m s^{- 1}

4

20 m s^{- 1}

Explanation:

For completing the full circle:
supporting img
$\frac{u}{2} = \sqrt{5 g L} \Rightarrow u = 4 {m s}^{- 1}$
Relative velocity $= 2 u = 8 {m s}^{- 1}$

PHXI06:WORK ENERGY AND POWER

355706 A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1 The mass is at the highest point

2 The wire is horizontal

3 The mass is at the lowest point

4 Inclined at an angle of

60^{\circ}

from vertical

NEET - 2019

PHXI06:WORK ENERGY AND POWER

355707 A bob of mass ' $m$ ' is suspended by a light string of length ' $L$ '. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$ . The ratio of kinetic energies $\frac{{(K . E .)}_{A}}{{(K . E .)}_{B}}$ is
supporting img

1

3 : 2

2

1 : 5

3

2 : 5

4

5 : 1

Explanation:

The critical velocity at $A$ is $v_{L} = \sqrt{5 g L}$ and at $B$ is $v_{H} = \sqrt{g L}$ .
$K E_{A} = \frac{1}{2} m v_{L}^{2} K E_{B} = \frac{1}{2} m v_{H}^{2}$
supporting img

So, $\frac{K E_{A}}{K E_{B}} = \frac{v_{L}^{2}}{v_{H}^{2}} = \frac{5 g L}{g L} = \frac{5}{1}$

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355708 With what minimum speed $v$ must a small ball should be pushed inside a smooth vertical tube from a height $h$ so that it may reach the top of the tube? Radius of the tube is $R$ .

1

\sqrt{g (5 R - 2 h)}

2

\sqrt{2 g (h + 2 R)}

3

\sqrt{2 g (2 R - h)}

4

\frac{5}{2} R

Explanation:

Velocity of a ball to just reach the top of the tube should be given by;
$0 = v^{2} - 2 g h_{0}$
Where the velocity will be zero at topmost point.
Here $h_{0} = (2 R - h)$
Thus $v = \sqrt{2 g (2 R - h)}$

PHXI06:WORK ENERGY AND POWER

355709 An insect jumps from ball $A$ onto ball $B$ . which are suspended from inextensible light strings each of length $L = 8 c m$ . The mass of each ball and insect is same. What should be the minimum relative velocity of jump of insect w.r.t. ball $A$ , if both the balls manage to complete the full circle?
supporting img

1

8 m s^{- 1}

2

4 m s^{- 1}

3

12 m s^{- 1}

4

20 m s^{- 1}

Explanation:

For completing the full circle:
supporting img
$\frac{u}{2} = \sqrt{5 g L} \Rightarrow u = 4 {m s}^{- 1}$
Relative velocity $= 2 u = 8 {m s}^{- 1}$

PHXI06:WORK ENERGY AND POWER

355706 A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1 The mass is at the highest point

2 The wire is horizontal

3 The mass is at the lowest point

4 Inclined at an angle of

60^{\circ}

from vertical

NEET - 2019

PHXI06:WORK ENERGY AND POWER

355707 A bob of mass ' $m$ ' is suspended by a light string of length ' $L$ '. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$ . The ratio of kinetic energies $\frac{{(K . E .)}_{A}}{{(K . E .)}_{B}}$ is
supporting img

1

3 : 2

2

1 : 5

3

2 : 5

4

5 : 1

Explanation:

The critical velocity at $A$ is $v_{L} = \sqrt{5 g L}$ and at $B$ is $v_{H} = \sqrt{g L}$ .
$K E_{A} = \frac{1}{2} m v_{L}^{2} K E_{B} = \frac{1}{2} m v_{H}^{2}$
supporting img

So, $\frac{K E_{A}}{K E_{B}} = \frac{v_{L}^{2}}{v_{H}^{2}} = \frac{5 g L}{g L} = \frac{5}{1}$

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355708 With what minimum speed $v$ must a small ball should be pushed inside a smooth vertical tube from a height $h$ so that it may reach the top of the tube? Radius of the tube is $R$ .

1

\sqrt{g (5 R - 2 h)}

2

\sqrt{2 g (h + 2 R)}

3

\sqrt{2 g (2 R - h)}

4

\frac{5}{2} R

Explanation:

Velocity of a ball to just reach the top of the tube should be given by;
$0 = v^{2} - 2 g h_{0}$
Where the velocity will be zero at topmost point.
Here $h_{0} = (2 R - h)$
Thus $v = \sqrt{2 g (2 R - h)}$

PHXI06:WORK ENERGY AND POWER

355709 An insect jumps from ball $A$ onto ball $B$ . which are suspended from inextensible light strings each of length $L = 8 c m$ . The mass of each ball and insect is same. What should be the minimum relative velocity of jump of insect w.r.t. ball $A$ , if both the balls manage to complete the full circle?
supporting img

1

8 m s^{- 1}

2

4 m s^{- 1}

3

12 m s^{- 1}

4

20 m s^{- 1}

Explanation:

For completing the full circle:
supporting img
$\frac{u}{2} = \sqrt{5 g L} \Rightarrow u = 4 {m s}^{- 1}$
Relative velocity $= 2 u = 8 {m s}^{- 1}$

PHXI06:WORK ENERGY AND POWER

355706 A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1 The mass is at the highest point

2 The wire is horizontal

3 The mass is at the lowest point

4 Inclined at an angle of

60^{\circ}

from vertical

NEET - 2019

PHXI06:WORK ENERGY AND POWER

355707 A bob of mass ' $m$ ' is suspended by a light string of length ' $L$ '. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$ . The ratio of kinetic energies $\frac{{(K . E .)}_{A}}{{(K . E .)}_{B}}$ is
supporting img

1

3 : 2

2

1 : 5

3

2 : 5

4

5 : 1

Explanation:

The critical velocity at $A$ is $v_{L} = \sqrt{5 g L}$ and at $B$ is $v_{H} = \sqrt{g L}$ .
$K E_{A} = \frac{1}{2} m v_{L}^{2} K E_{B} = \frac{1}{2} m v_{H}^{2}$
supporting img

So, $\frac{K E_{A}}{K E_{B}} = \frac{v_{L}^{2}}{v_{H}^{2}} = \frac{5 g L}{g L} = \frac{5}{1}$

JEE - 2024

PHXI06:WORK ENERGY AND POWER

355708 With what minimum speed $v$ must a small ball should be pushed inside a smooth vertical tube from a height $h$ so that it may reach the top of the tube? Radius of the tube is $R$ .

1

\sqrt{g (5 R - 2 h)}

2

\sqrt{2 g (h + 2 R)}

3

\sqrt{2 g (2 R - h)}

4

\frac{5}{2} R

Explanation:

Velocity of a ball to just reach the top of the tube should be given by;
$0 = v^{2} - 2 g h_{0}$
Where the velocity will be zero at topmost point.
Here $h_{0} = (2 R - h)$
Thus $v = \sqrt{2 g (2 R - h)}$

PHXI06:WORK ENERGY AND POWER

355709 An insect jumps from ball $A$ onto ball $B$ . which are suspended from inextensible light strings each of length $L = 8 c m$ . The mass of each ball and insect is same. What should be the minimum relative velocity of jump of insect w.r.t. ball $A$ , if both the balls manage to complete the full circle?
supporting img

1

8 m s^{- 1}

2

4 m s^{- 1}

3

12 m s^{- 1}

4

20 m s^{- 1}

Explanation:

For completing the full circle:
supporting img
$\frac{u}{2} = \sqrt{5 g L} \Rightarrow u = 4 {m s}^{- 1}$
Relative velocity $= 2 u = 8 {m s}^{- 1}$

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