Question

What is the accelerations of the objects? What is the tension of the string? What is the speed of each object 1.00 sec ?

Answer 1

Considering the string to be light and inextensible,we can say tension in the string will be the same for holding the two objects.

Let,tension in the string is `T`

Now,for `m_2` `T` is acting against `m_2g sin 60`

And,for `m_1` tension acts against `m_1g`

Clearly, `m_1g < m_2g sin 60` (from the given values of mass)

So,`m_2` will go downwards along the plane and `m_1` will go upwards.

So,`m_1` we can write,

`T- m_1g=m_1a` (where, `a` is the acceleration of both the mass)

And,for `m_2`

`m_2 g sin 60 - T=m_2a`

Solving both the equations,we get,

`a=(2.5sqrt(3) -2)/7 g=3.25 ms^-2`

So, `T=26.1 N`

Velocity of `m_1` and `m_2` after `1s` will be `(3.25×1)=3.25ms^-1` (using, `v=u+at`,here,`u=0`)