Question

Two smooth blocks of masses $m$ and $3 m$ are connected by an inextensible light string. If forces $F$ and $2 F$ act on the blocks, find

$(a)$ tension in the string, and

$(b)$ acceleration of the blocks.

Accepted Answer

Both the blocks will move in a rightwards direction with the same acceleration.

The free-body diagrams of both the blocks and

Now using Newton's second law of motion, $\sum F_{x} = m a_{x}$

From F.B.D of $(b)$

From F.B.D of $3 m : 2 F - T = 3 m a . . . (ii)$

Solving equations $(i)$ and $(ii)$ , $T = \frac{5 F}{4}$ .

$(b)$ Both the blocks will move in a rightwards direction with the same acceleration.

The free-body diagrams of both the blocks and

Now using Newton's second law of motion, $\sum F_{x} = m a_{x}$

From F.B.D of $m : T - F = m a . . . (i)$

From F.B.D of $3 m : 2 F - T = 3 m a . . . (ii)$

Solving equations $(i)$ and $(ii)$ , $a = \frac{F}{4 m}$ .

B M Sharma Solutions for Chapter: Newton's Laws of Motion (Without Friction), Exercise 29: ILLUSTRATION 6.26

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Newton's Laws of Motion (Without Friction), Exercise 29: ILLUSTRATION 6.26