Question

A trolley of mass rn = 5kg is connccted to a block of mass m = 2kg with thc help

of massless inextensiblc spring passing ovcr a light frictionless pulley as shown

in the figurc. Find thc tcnsion in the string.

(Assumc no frictiorl, g = 10ms-2 sin 53" = { una cos 53o = Jl​

Answer 1

Given that,

Mass of trolley = 5 kg

Mass of block = 2 kg

Angle = 53°

For truck,

We need to calculate the tension in the string

Using balance equation

$T=ma$

$T=5a$....(I)

For block,

We need to calculate the tension in the string

Using balance equation

$mg\sin\theta-T=ma$

Where, m = mass

g = acceleration due to gravity

Put the value into the formula

$20\sin53-T=2a$....(II)

We need to calculate the tension

Using equation (I) and (II)

$20\times\dfrac{4}{5}=7a$

$a=2.28\ m/s^2$

We need to calculate the tension in the string

Using equation (I)

$T=5a$

Put the value of a

$T=5\times2.28$

$T=11.4\ N$

Hence, The tension in the string is 11.4 N.