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Free-Body Diagrams - FBD

Two particles of mass m each are tied at the ends of a light s

Question

Hard

Solving time: 4 mins

Two particles of mass $m$ each are tied at the ends of a light string of length $2 a$ . The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ' $a$ ' from the center $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$ . As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2 x$ , is
$-$

$-$

\frac{F}{2 m} \frac{a}{a ^{2} - x ^{2}}

\frac{F}{2 m} \frac{x}{a ^{2} - x ^{2}}

\frac{F}{2 m} \frac{x}{a}

\frac{F}{2 m} \frac{a ^{2} - x ^{2}}{x}

Views: 5,771 students

Updated on: Nov 7, 2023

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Owen Discussed

Two particles of mass

m

each are tied at the ends of a light string of length

2 a

. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance '

a

' from the center

P

(as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force

F

. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes

2 x

, is

-

-

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

The arrangement is shown in the figure. The separation between the two masses is

2 x

. Each mass will move in the horizontal direction as shown in the figure.

-

-

Let the tension in the string be

T

. The forces acting at point

P

and on one of the masses are shown in the figure.
Net force at point

P

must equal zero.

∴ 2 T sin θ = F \dots (i)

-

-

Also, for the mass

m, N + T sin θ - m g = 0 \dots (ii)

and

T cos θ = m A

Equations (i) and (iii) give

A = \frac{F c o t θ}{2 m} = \frac{F}{2 m} (\frac{x}{a ^{2} - x ^{2}})

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Question Text	Two particles of mass $m$ each are tied at the ends of a light string of length $2 a$ . The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ' $a$ ' from the center $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$ . As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2 x$ , is $-$ $-$
Updated On	Nov 7, 2023
Topic	Laws of motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 12
Upvotes	1263
Avg. Video Duration	7 min

Text solutionVerified

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