Two masses of 40 kg and 30 kg are connected by a weightless string passing over a frictionless pulley as shown in the figure. The acceleration of the system would be

Options

A. `0.7 ms^(-2)`
B. `0.8 ms^(-2)`
C. `0.6 ms^(-2)`
D. `0.5 ms^(-2)`

Answer

A

Explanation

Here,` m_1 = 40 kg, m_2 = 30 kg, theta = 30^@`

Let T be the tension in the string and a be the acceleration of the system of two masses.
Their equations of motion are
`m_1a = m_1 g sin 30^@ `
` m_2 a T -m_2 g sin 30^@`
Adding (i) and (ii), we get
`(40 +30)a= (40 -30) xx 9.8 xx 1/2 =49 or a = (49 )/( 70 ) = 0.7 ms^(-2)`