A spring balance has a scale which ranges from 0 to 25 kg and the length of the scale is 0.25 m. It is taken to an unknown planet X where the acceleration due to gravity is 11.5ms^(-1). Suppose a body a mass M kg is suspended in this spring and made to oscillate with a period of 0.50 s. Compute the gravitational force acting on the body.

A spring balance has a scale which ranges from 0 to 25 kg and the leng

1.	A spring balance has a scale which ranges from 0 to 25 kg and the length of the scale is 0.25 m. It is taken to an unknown planet X where the acceleration due to gravity is 11.5ms^(-1). Suppose a body a mass M kg is suspended in this spring and made to oscillate with a period of 0.50 s. Compute the gravitational force acting on the body.
Answer» Solution :Let us first calculate the stiffness constant of the spring balance by USING equation `(m)/(k)=(l)/(g)` `k=(mg)/(l)=(25xx11.5)/(0.25)=1150Nm^(-1)` The time period of oscillations is given by `T=2pisqrt((M)/(k))`, where M is the mass of the BODY. Since, M is unknown, rearranging, we get `M=(KT^(2))/(4pi^(2))=((1150)(0.5)^(2))/(4pi^(2))=7.3kg` `M=(kT^(2))/(4pi^(2))=((1150)(0.5)^(2))/(4pi^(2))=7.3kg` The GRAVITATIONAL force ACTING on the body is `W=Mg=7.3xx11.5=83.95N~~84N`