Question

two masses m1 and m2 are attached to the end of a string which passes over a pulley attached to the top of an inclined plane .the angle of inclination of the plane theta .if m1=10kg , m2=5kg, theta =30 .then what is the tension in the string?
a.100N b.50N c.25N d.zero

Answer 1

In the figure, from the FBD of the 10 kg mass, when we consider the forces parallel to the surface of the plane, we get,

$\sf{\longrightarrow T-50=10a\quad\quad\dots(1)}$

Here 10a is the net force acting on the 10 kg mass, where a is the net acceleration of the system.

From the FBD of the 5 kg mass, when we consider the vertical forces, we get,

$\sf{\longrightarrow 50-T=5a\quad\quad\dots(2)}$

Here 5a is the net force.

Adding (1) and (2),

$\sf{\longrightarrow T-50+50-T=10a+5a}$

$\sf{\longrightarrow15a=0}$

$\sf{\longrightarrow a=0}$

Then (1) becomes,

$\sf{\longrightarrow T-50=0}$

$\sf{\longrightarrow\underline{\underline{T=50\ N}}}$

Hence (b) is the answer.