Two masses m1 and m2 are attached to a string which passes over a frictionless smooth pulley. When m1 = 10 kg , m2 = 6kg, the acceleration of masses is

The correct option is 2.5 ms⁻².

Step-by-step Explanation:

We are given a system of two masses connected by a string passing over a frictionless, smooth pulley (an Atwood machine).

Let the given masses be:
$m_1=10kg$
$m_2=6kg$

Since $m_1>m_2$, the mass $m_1$ will accelerate downwards, and the mass $m_2$ will accelerate upwards with the same acceleration a.

Let T be the tension in the string and g be the acceleration due to gravity. Using the standard value $g=10m{s}^{-2}$.

Writing the equations of motion for both masses:
For the downward moving mass $m_1$:
$m_{1}g-T=m_{1}a$ (Equation 1)

For the upward moving mass $m_2$:
$T-m_{2}g=m_{2}a$ (Equation 2)

Adding Equation 1 and Equation 2 to eliminate tension T:
$(m_1-m_2)g=(m_1+m_2)a$

Now, solving for the acceleration a:
$a=\frac{m_1-m_2}{m_1+m_2}g$

Substituting the given values:
$a=\frac{10-6}{10+6}\times 10$

$a=\frac{4}{16}\times 10$

$a=\frac{1}{4}\times 10$

$a=2.5m{s}^{-2}$

Thus, the acceleration of the masses is 2.5 ms⁻².