Answer:
The distance of the object to the center of the earth increases.
Explanation:
The acceleration due to gravity on Earth is given by:
where
G is the gravitational constant
M is the Earth's mass
r is the distance of the object from the Earth's centre
We notice that:
- g does not depend on the mass of the object
- g is inversely proportional to r
This means that if the distance of the object from the Earth's centre increases, g decreases. So, the correct option is
The distance of the object to the center of the earth increases.
Take the derivative to find the velocity of the object:
The object stops when 
:
so the answer is E.
Answer:
Explanation:
Due to heat energy , metal expands . Formula for linear expansion is as follows .
L = l ( 1 + α Δt )
where L is expanded length , l is original length , α is coefficient of linear expansion and Δt is increase in temperature .
To pass the sphere through the ring , the diameter of both ring and sphere should be same after heating . Let after increase of temperature Δt , their diameter becomes same as L . The linear coefficient of brass and steel are
20 x 10⁻⁶ and 12 x 10⁻⁶ respectively .
For steel sphere ,
L = 25 ( 1 + 12 x 10⁻⁶ Δt )
For brass ring
L = 24.9 ( 1 + 20 x 10⁻⁶ Δt )
25 ( 1 + 12 x 10⁻⁶ Δt ) = 24.9 ( 1 + 20 x 10⁻⁶ Δt )
1.004( 1 + 12 x 10⁻⁶ Δt ) = ( 1 + 20 x 10⁻⁶ Δt )
1.004 + 12.0482 x 10⁻⁶ Δt = 1 + 20 x 10⁻⁶ Δt
.004 = 7.9518 x 10⁻⁶ Δt
Δt = 4000 / 7.9518
= 503⁰C.
final temp = 503 + 15 = 518⁰C .
True. That is how powerful the sun is. But it will explode in only about 5 billion years.
The cyclist who travels 20 kilometers per hour for 15 kilometers
