Question

two masses 2kg and 4kg are connected at the 2 ends of light inextensible string passing over a frictionless pulley. if the masses are released, then find the acceleration of the masses and the tension in the string

Answer 1

$\text{\underline{\underline{Given:}}}$

$\sf{m_{1} = 4 \: kg}$

$\sf{m_{2} = 2 \: kg}$

$\sf{g = 10 {m/s}^{2}}$


Now,

$\text{\underline{We\:know\:that:}}$

When the masses are released, then the masses move with common magnitude of acceleration a.

$\boxed{a = \frac{m_{1} - m_{2} }{m_{1} + m_{2} } g}$


By substituting the above values in this formula,

$\text{\underline{We\:get:}}$

$\sf{a = \frac{m_{1} - m_{2}}{m_{1} + m_{2}}} g$

$\sf{a = \frac{4 - 2}{4 + 2} \times 10}$

$\sf{a = \frac{2}{6} \times 10}$

$\boxed{a = 3.33 \: {m/s}^{2}}$


And,

$\text{\underline{Tension\:T in\:the\:string\:is:}}$

$\sf{T = \frac{2m_{1}m_{2}}{m_{1} + m_{2}} \times g}$

$\sf{T = \frac{2 \times 4 \times 2}{2 + 4} \times 10}$

$\sf{T = \frac{16}{6} \times 10}$

$\sf{T = \frac{16}{3} \times 5}$

$\boxed{T = 26.67 \: N}$

Answer 2

◆$\sf\huge{\boxed{\underline{Answer}}}$◆

Given▶

m1 = 2kg

m2 = 4kg

g = 10$m/s^{2}$

Let T be the tension in the string due to the two masses!

we have!

weight of 2kg block < Tension in the string!

this can be represented as

T - m1(g) = $m1\times a$==(1)

SIMILARLY,

weight of 4kg block is greater than Tension in the string , it is given by!

m2(g) - T = $m2\times a$=(2)

Note!!

____________

We are subtracting the tension from the weight because both are acting in opposite direction i.e, weight acting in downwards , while Tension acting along the length!.

____________

subtracting equation (1)&(2)

T - m1(g) = $m1\times a$

-T + m2(g) = $m2\times a$

we get!

g(m2 - m1) = a(m2+m1)

10(4-2) = a (4+2)

$\frac{10\times 2}{6}$= a

a = $\frac{20}{6}$

a = 3.33$m/s^{2}$

substituting values of 'a' in equation (1), we get!

T = m1(g)+ m1(a)

T = m1(g+a)

= 2(10+3.33)

= $2\times 13.33$

= 26.66N is the tension in the string!

and the acceleration of the masses is

3.33$m/s^{2}$