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Work, Energy and Power

268909 A test tube of mass $20 gm$ is filled with a gas and fitted with a stopper of $2 gm$ . It is suspended horizontally by means of a thread of $1 m$ length and heated. When the stopper kicks out, the tube just completes a circle in vertical plane. The velocity with which the stopper kicked out is

1

7 {ms}^{- 1}

2

10 {ms}^{- 1}

3

70 {ms}^{- 1}

4

0.1 {ms}^{- 1}

Explanation:

$M \sqrt{5 g l} = m v$

Work, Energy and Power

268910 Two bodies move towards each other and collide inelastically. The velocity of the first body is $2 m / s$ and that of the second is $4 m / \sec$ before impact.The common velocity after collision is $1 m / s$ in the direction of the first body. The number of times did the KE of the first body exceed that of the second body before collision.

1 4.25

2 3.253

3 2.25

4 1.25

Explanation:

Calculate $K \cdot E_{1}$ and $K . E_{2}$ before collision $∴ n = \frac{K \cdot E_{1}}{K \cdot E_{2}}$

Work, Energy and Power

268911 Three particles $A, B$ and $C$ of equal masses, moving with the same speed ' $v$ ' along the medians of an equilateral triangle, collide at the centroid G of the triangle. After collision, A comes to rest and $B$ retraces its path with a speed ' $v$ '. The speed of $C$ after the collision is

1

v

along

B G

2

\frac{v}{2}

along

GB

3 Zero

4

v

along

C G

Explanation:

Along $X$ - axis:
$0 + m v \cos θ - m v \cos θ = 0 - m v \cos θ + m v_{x}$
$v_{x} = v \cos θ (θ = 30^{\circ})$
Along $Y$ - axis:
$- m v + m v \sin θ + m v \sin θ = 0 - m v \sin θ + m v_{y}$ $v_{y} = v \sin θ (θ = 30^{\circ}); v_{n e t} = \sqrt{v_{x}^{2} + v_{y}^{2}}$

Work, Energy and Power

268912 A moving sphere $P$ collides another sphere $Q$ at rest. If the collision takes place along the line joining their centers of mass such that their total kinetic energy is conserved and the fraction of K.E. transferred by the colliding particle is $\frac{8}{9}$ , then the mass of $P$ and the mass of $Q$ bears a ratio

1

\sqrt{8} : 3

2

9 : 8

3

2 : 3

4

2 : 1

Explanation:

$\frac{4 m_{1} m_{2}}{{(m_{1} + m_{2})}^{2}} = \frac{8}{9}$ , find $m_{1}$ and $m_{2}$

Work, Energy and Power

268909 A test tube of mass $20 gm$ is filled with a gas and fitted with a stopper of $2 gm$ . It is suspended horizontally by means of a thread of $1 m$ length and heated. When the stopper kicks out, the tube just completes a circle in vertical plane. The velocity with which the stopper kicked out is

1

7 {ms}^{- 1}

2

10 {ms}^{- 1}

3

70 {ms}^{- 1}

4

0.1 {ms}^{- 1}

Explanation:

$M \sqrt{5 g l} = m v$

Work, Energy and Power

268910 Two bodies move towards each other and collide inelastically. The velocity of the first body is $2 m / s$ and that of the second is $4 m / \sec$ before impact.The common velocity after collision is $1 m / s$ in the direction of the first body. The number of times did the KE of the first body exceed that of the second body before collision.

1 4.25

2 3.253

3 2.25

4 1.25

Explanation:

Calculate $K \cdot E_{1}$ and $K . E_{2}$ before collision $∴ n = \frac{K \cdot E_{1}}{K \cdot E_{2}}$

Work, Energy and Power

268911 Three particles $A, B$ and $C$ of equal masses, moving with the same speed ' $v$ ' along the medians of an equilateral triangle, collide at the centroid G of the triangle. After collision, A comes to rest and $B$ retraces its path with a speed ' $v$ '. The speed of $C$ after the collision is

1

v

along

B G

2

\frac{v}{2}

along

GB

3 Zero

4

v

along

C G

Explanation:

Along $X$ - axis:
$0 + m v \cos θ - m v \cos θ = 0 - m v \cos θ + m v_{x}$
$v_{x} = v \cos θ (θ = 30^{\circ})$
Along $Y$ - axis:
$- m v + m v \sin θ + m v \sin θ = 0 - m v \sin θ + m v_{y}$ $v_{y} = v \sin θ (θ = 30^{\circ}); v_{n e t} = \sqrt{v_{x}^{2} + v_{y}^{2}}$

Work, Energy and Power

268912 A moving sphere $P$ collides another sphere $Q$ at rest. If the collision takes place along the line joining their centers of mass such that their total kinetic energy is conserved and the fraction of K.E. transferred by the colliding particle is $\frac{8}{9}$ , then the mass of $P$ and the mass of $Q$ bears a ratio

1

\sqrt{8} : 3

2

9 : 8

3

2 : 3

4

2 : 1

Explanation:

$\frac{4 m_{1} m_{2}}{{(m_{1} + m_{2})}^{2}} = \frac{8}{9}$ , find $m_{1}$ and $m_{2}$

Work, Energy and Power

268909 A test tube of mass $20 gm$ is filled with a gas and fitted with a stopper of $2 gm$ . It is suspended horizontally by means of a thread of $1 m$ length and heated. When the stopper kicks out, the tube just completes a circle in vertical plane. The velocity with which the stopper kicked out is

1

7 {ms}^{- 1}

2

10 {ms}^{- 1}

3

70 {ms}^{- 1}

4

0.1 {ms}^{- 1}

Explanation:

$M \sqrt{5 g l} = m v$

Work, Energy and Power

268910 Two bodies move towards each other and collide inelastically. The velocity of the first body is $2 m / s$ and that of the second is $4 m / \sec$ before impact.The common velocity after collision is $1 m / s$ in the direction of the first body. The number of times did the KE of the first body exceed that of the second body before collision.

1 4.25

2 3.253

3 2.25

4 1.25

Explanation:

Calculate $K \cdot E_{1}$ and $K . E_{2}$ before collision $∴ n = \frac{K \cdot E_{1}}{K \cdot E_{2}}$

Work, Energy and Power

268911 Three particles $A, B$ and $C$ of equal masses, moving with the same speed ' $v$ ' along the medians of an equilateral triangle, collide at the centroid G of the triangle. After collision, A comes to rest and $B$ retraces its path with a speed ' $v$ '. The speed of $C$ after the collision is

1

v

along

B G

2

\frac{v}{2}

along

GB

3 Zero

4

v

along

C G

Explanation:

Along $X$ - axis:
$0 + m v \cos θ - m v \cos θ = 0 - m v \cos θ + m v_{x}$
$v_{x} = v \cos θ (θ = 30^{\circ})$
Along $Y$ - axis:
$- m v + m v \sin θ + m v \sin θ = 0 - m v \sin θ + m v_{y}$ $v_{y} = v \sin θ (θ = 30^{\circ}); v_{n e t} = \sqrt{v_{x}^{2} + v_{y}^{2}}$

Work, Energy and Power

268912 A moving sphere $P$ collides another sphere $Q$ at rest. If the collision takes place along the line joining their centers of mass such that their total kinetic energy is conserved and the fraction of K.E. transferred by the colliding particle is $\frac{8}{9}$ , then the mass of $P$ and the mass of $Q$ bears a ratio

1

\sqrt{8} : 3

2

9 : 8

3

2 : 3

4

2 : 1

Explanation:

$\frac{4 m_{1} m_{2}}{{(m_{1} + m_{2})}^{2}} = \frac{8}{9}$ , find $m_{1}$ and $m_{2}$

Work, Energy and Power

268909 A test tube of mass $20 gm$ is filled with a gas and fitted with a stopper of $2 gm$ . It is suspended horizontally by means of a thread of $1 m$ length and heated. When the stopper kicks out, the tube just completes a circle in vertical plane. The velocity with which the stopper kicked out is

1

7 {ms}^{- 1}

2

10 {ms}^{- 1}

3

70 {ms}^{- 1}

4

0.1 {ms}^{- 1}

Explanation:

$M \sqrt{5 g l} = m v$

Work, Energy and Power

268910 Two bodies move towards each other and collide inelastically. The velocity of the first body is $2 m / s$ and that of the second is $4 m / \sec$ before impact.The common velocity after collision is $1 m / s$ in the direction of the first body. The number of times did the KE of the first body exceed that of the second body before collision.

1 4.25

2 3.253

3 2.25

4 1.25

Explanation:

Calculate $K \cdot E_{1}$ and $K . E_{2}$ before collision $∴ n = \frac{K \cdot E_{1}}{K \cdot E_{2}}$

Work, Energy and Power

268911 Three particles $A, B$ and $C$ of equal masses, moving with the same speed ' $v$ ' along the medians of an equilateral triangle, collide at the centroid G of the triangle. After collision, A comes to rest and $B$ retraces its path with a speed ' $v$ '. The speed of $C$ after the collision is

1

v

along

B G

2

\frac{v}{2}

along

GB

3 Zero

4

v

along

C G

Explanation:

Along $X$ - axis:
$0 + m v \cos θ - m v \cos θ = 0 - m v \cos θ + m v_{x}$
$v_{x} = v \cos θ (θ = 30^{\circ})$
Along $Y$ - axis:
$- m v + m v \sin θ + m v \sin θ = 0 - m v \sin θ + m v_{y}$ $v_{y} = v \sin θ (θ = 30^{\circ}); v_{n e t} = \sqrt{v_{x}^{2} + v_{y}^{2}}$

Work, Energy and Power

268912 A moving sphere $P$ collides another sphere $Q$ at rest. If the collision takes place along the line joining their centers of mass such that their total kinetic energy is conserved and the fraction of K.E. transferred by the colliding particle is $\frac{8}{9}$ , then the mass of $P$ and the mass of $Q$ bears a ratio

1

\sqrt{8} : 3

2

9 : 8

3

2 : 3

4

2 : 1

Explanation:

$\frac{4 m_{1} m_{2}}{{(m_{1} + m_{2})}^{2}} = \frac{8}{9}$ , find $m_{1}$ and $m_{2}$

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