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In the figure masses 400 {~kg} and 100 {~kg} are fixed. [https

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In the figure masses $400 kg$ and $100 kg$ are fixed. (a) How much work must be done to move a $1 kg$ mass from point $A$ to point $B$ ? (b) What is the minimum kinetic energy with which the $1 kg$ mass must be projected from $A$ to the right to reach the point $B$ ?

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Mechanics Volume 2 (DC Pandey)

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In the figure masses

400 kg

and

100 kg

are fixed.

(a) How much work must be done to move a

1 kg

mass from point

A

to point

B

? (b) What is the minimum kinetic energy with which the

1 kg

mass must be projected from

A

to the right to reach the point

B

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

(a)

W = U_{f} - U_{i} = U_{B} - U_{A}

= m V_{B} - m V_{A} (V = gravitational potential)

= m (V_{B} - V_{A})

= (1) [- \frac{100}{2} - \frac{400}{8} + \frac{100}{8} + \frac{400}{2}] (6.67 \times 1 0^{- 11})

= 7.5 \times 1 0^{- 9} J

(b) First let us find the point (say)

c

between

A

and

B

where field strength due to

400 kg

and

100 kg

masses is zero.
Let its distance from

400 kg

r

. Then,

\frac{G ( 400 )}{r ^{2}} = \frac{G ( 100 )}{( 10 - r ) ^{2}}

r = \frac{20}{3} m

and

(10 - r) = \frac{10}{3} m

So, we have to move the body only from

A

C

. After that

100 kg

mass will pull

1 kg

mass by its own.

∴

Minimum kinetic energy

= Δ U = U_{C} - U_{A}

= m (V_{C} - V_{A})

= (1) [- \frac{400}{20/3} - \frac{100}{10/3} + \frac{100}{8} + \frac{400}{2}] (6.67 \times 1 0^{- 11})

= 8.17 \times 1 0^{- 9} J

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Question Text	In the figure masses $400 kg$ and $100 kg$ are fixed. (a) How much work must be done to move a $1 kg$ mass from point $A$ to point $B$ ? (b) What is the minimum kinetic energy with which the $1 kg$ mass must be projected from $A$ to the right to reach the point $B$ ?
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	144

In the figure masses $400 kg$ and $100 kg$ are fixed. (a) How much work must be done to move a $1 kg$ mass from point $A$ to point $B$ ? (b) What is the minimum kinetic energy with which the $1 kg$ mass must be projected from $A$ to the right to reach the point $B$ ?

Text solutionVerified

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In the figure masses 400 kg and 100 kg are fixed. (a) How much work must be done to move a 1 kg mass from point A to point B ? (b) What is the minimum kinetic energy with which the 1 kg mass must be projected from A to the right to reach the point B ?

Text solutionVerified

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In the figure masses $400 kg$ and $100 kg$ are fixed. (a) How much work must be done to move a $1 kg$ mass from point $A$ to point $B$ ? (b) What is the minimum kinetic energy with which the $1 kg$ mass must be projected from $A$ to the right to reach the point $B$ ?