Question

a body of mass 5kg lies on a horizontal frictionless plane. A string attached to its passes over a smooth pulley fixed to the edge of the plane and carries a load of mass 1kg. Find the acceleration of the system​

Answer 1

Answer:-

a = 1.66 m/s²

Given :-

$m_1 = 1kg \\ m_2 = 5kg$

To find :-

The acceleration of the system.

Solution:-

Since, pulleys and plane is frictionless and massless.

Let $m_1 , m_2$ be the mass of each block.

• For block $m_1$

Force acting on the block are :-

• Tension force upward.
• Gravitational force downward.

But acceleration is in downward direction.

$\mathsf{F_{Net} = m_1g - T}$

$\mathsf{m_1a = m_1 g -T}$

$\mathsf{ T = m_1g - m_1a}------1)$

• For block of mass $m_2$

→$\mathsf{ T = m_2a}-----2)$

• Tension force is equal because string is massless.

• From eq. 1 and 2.

→$\mathsf{m_2a = m_1g - m_1a}$

→$\mathsf{m_2a + m_1 a = m_1g }$

→$\mathsf{a ( m_2 + m_1) = m_1 g }$

→$\mathsf{a =\left( \dfrac{m_1g}{m_2 + m_1}\right)}$

• Put the given values,

→$\mathsf{a = \left(\dfrac{1 \times 10}{5+1}\right) }$

→$\mathsf{a = \dfrac{10}{6}}$

→$\mathsf{a = 1.66 m/s^2 }$

hence,

The acceleration of the whole system is 1.66 m/s².

Answer 2

Answer:

1.66 m/s^2 is the acceleration.