Question

Calculate the acceleration of the masses shown in the figure and also
find the tension in the strings
connecting the two masses. The
strings are light and inextensible,
the pulleys are also light and
frictionless. Take m1 = 4kg,
m2 = 12 kg and g = 9.8 m/sec²

Answer 1

Given :

➡Mass of First object ( m1 ) = 4 kg

➡Mass of Second object ( m2 ) = 12 kg

➡Acceleration due to gravity ( g ) = 9.8 m/s²

To Find :

➡Acceleration = ?

➡Tension = ?

Solution :

We know that ,

$\large \fbox{ \bold{ a = \frac{m1 \: - \: m2}{m1 \: + \: m2} \times g}}$

$\large \fbox{\bold{t = \frac{2m1m2}{m1 + m2} \times g }}$

Therefore ,

$\to \: a = \frac{4 - 12}{4 + 12} \times 9.8 \\ \\ \to a = \frac{8}{16} \times 9.8 \\ \\ \to a = 0.5 \times 9.8 \\ \\ \to a = 4.9 \: \: m/{s}^{2}$

_____________________

$\to t = \frac{2 \: \times \: 4 \: \times \: 12}{4 \: + \: 12} \times 9.8 \\ \\ \to t = \frac{96}{16} \times 9.8 \\ \\ \to t = 6 \: \times \: 9.8 \\ \\ \to t = 58.8 \: \: N$