Out of the two spheres of equal mass one rolls down a smooth inclined plane while other is freely falling both from same height . in which case is the work done more? why?

In case of sphere rolls down a smooth inclined plane , work is done by gravity only as in free fall but as it is inclined

So, there comes a factor sin( angle of inclination)

So acceleration becomes g sin( angle of inclination)

Now , As in free fall acceleration is g

And max value of Sin is 1

So ,range of acceleration in smooth inclined plane varies from 0 to g

that is max acceleration or max work done as Work = m × acceleration × displacement

= mg sin ( angle) × displacement

As sin( angle) = height/displacement

So it becomes mg× height

In free fall, Work done = mg × height

So, Free fall work done is same as work done in smooth inclined plane

So, Work done in free fall = work done in smooth inclined plane

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50

d is the correct answer