Question

Find the ratio gravitational potential energy if the height of the object is doubled and its mass is tripled also find tge ratio of work done by gravity in bringing the object to zero height in both cases.

Answer 1

please see the attached document ..........
 i hope it helps..............

6f09322f99ccb12cf5cac5197e58275c.docx

Answer 2

Ratio of potential energy,

Potential energy in the 1st case,

Ep = mgh

Ep = mg2h ………….if height is doubled ………. (1)

Potential energy in the 2nd case,

Ep = mgh

Ep = mg3h ………...if the height is tripled ……… (2)

From (1) and (2)

Ratio of their potential energy,

= mg2h / mg3h

= 2mgh / 3mgh

= 2/3

Therefore the ratio = 2 : 3

Now,

Ratio of work done,

Work done in the 1st case,

W = fs

W = f * 2s ……..since the distance was doubled ……….. (1)

W = 2fs

Work done in the 2nd case,

W = fs

W = f * 3s………..since the distance is tripled ………….. (2)

W = 3fs

From (1) and (2)

Ratio of their work done,

= 2fs / 3fs

= 2 / 3