Three masses of 1 kg, 6 kg and 3 kg are connected to each other with strings and are placed on a table as shown in figure. What is the acceleration with which the system is moving? (Take g = 10 `m s^(-2)` )

Options

A. zero
B. ` 1 ms^(-2)`
C. `2 ms^(-2)`
D. `3 ms^(-2)`

Answer

C

Explanation

here ` ,m_1 = kg ,m_2 = 6kg and m_3 =3 kg `
Let a be the acceleration with which the system is moving. The equations of motion of three masses are
`m_1 a=T_1 -m_1 g `
` m_2 a =T_2 -T_1 `
` m_3 a = m3 g -T_2`
Adding (i), (ii) and (iii), we get
`a(m_1 +m_2 +m_2) =(m_3 -m_1) g `
` therefore a=((m_3 -m_1 )g)/((m_1+m_2 +m_3)) = ((3-1 ) xx 10 )/( 1+6+3 ) = 2 ms^(-2)`