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Two balls of masses m(1)=5kg, m(2)=10kg ...

Two balls of masses `m_(1)=5kg, m_(2)=10kg` are connected by a light inextensible string. A horizontal force F = 15 N is acting on the ball `m_(2)` along the line joining two balls as shown. What is the (a) acceleration of the balls (b) tension in the string?

Text Solution

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From the F.B.D. of `m_(1)`,
`N_(1)=m_(1)g " " ...(1)`
`T=m_(1)a" " ...(2)`
From the F.B.D. of `m_(2)`,
`N_(2)=m_(2)g " " ...(3)`
`F-T=m_(2)a" " ...(4)`
(a) Therefore from (2) and (4)
`F=(m_(1)+m_(2))a`
`therefore a=(F)/(m_(1)+m_(2))=(15)/(15)m//s^(2)=1m//s^(2)`
(b) `T=(m_(1)F)/(m_(1)+m_(2))=5N`.
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