Question

figure shows a block of mass 2m sliding on a block of mass m. find the acceleration of each block( all the surface are smooth) ​

Answer 1

Given:

Figure shows a block of mass 2m sliding on a block of mass m.

To find:

Acceleration of the blocks ?

Calculation:

For the 2m block:

$\rm \therefore \: (2m)g \sin( \theta) - T = (2m)a$

For the m block:

$\rm \therefore \: T - mg \sin( \theta) = ma$

Adding the equations:

$\rm \therefore \: 2mg \sin( \theta) - mg \sin( \theta) = 2ma + ma$

$\rm \implies \: mg \sin( \theta) = 3ma$

$\rm \implies \: g \sin( \theta) = 3a$

$\rm \implies \:a = \dfrac{ g \sin( \theta) }{3}$

$\rm \implies \:a = \dfrac{ g \sin( {30}^{ \circ} ) }{3}$

$\rm \implies \:a = \dfrac{ g \times (\frac{1}{2}) }{3}$

$\rm \implies \:a = \dfrac{g}{6}$

So, acceleration of the blocks is g/6 m/s².

Answer 2

Answer:

5/3 m/s^2

Explanation:

put the value of g=10 then answer comes correct.