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In the arrangement shown in fig. The str...

In the arrangement shown in fig. The strings are light and inextensible. The surface over which blocks are placed is smooth. Find:

(a) the acceleration of each block.
(b) the tension in each string.

A

`a = 4 ms^-2` `b = 16N` , `24N`

B

`a = 6 ms^-2` `b = 12N` , `24N`

C

`a = -4 ms^-2` `b = 16N` , `12N`

D

`a = -5 ms^-2` `b = 26N` , `24N`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Let a be the acceleration of each block and `T_(1)` and `T_(2)` be the tension, in the two strings as shown in fig.

Taking the three blocks and the two strings as the system

Using `Sigma F_(x)=ma_(x)`
or, `28=(4+2+1)a`
or, `a=(28)/(7)=4ms^(-2)`
(b) Free-body diagrams (showing the forces in x-direction only) of 4-kg block and 1-kg are shown in fig.

Using `Sigma F_(x)=ma_(x)`
For 1-kg block: `F-T_(1)=(1)(a)`
or `28-T_(1)=(1)(4)=4`
`implies T_(1)=28-4=24N`
For 4-kg blocks : `T_(2)=(4)(a)`
`rArr T_(2)=(4)(4)=16N`.
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