A cylindrical bar that us well insulated around its sides connects hot and cold reservoirs and conducts heat at a rate of 10.0 J/s under steady state conditions. If all of its linear dimensions (diameter and length) are reduced by half, the rate at which it will now conduct heat between the same reservoirs is closest to

the at which the bar conducts now is 5 Js⁻¹

Explanation:

Given the data in the question;

we know that; Heat transfer by conduction is given by;

Q ∝

such that,

=

so

( 10 Js⁻¹ × π()² × ) / (πr² × )  

( 10 Js⁻¹ × π() × ) / (πr² × )

( 10 Js⁻¹ × πr² × 1/4 × ) / (πr² × 1/2 × )

( 10 Js⁻¹ × 1/4) / ( 1/2)

 ( 10 Js⁻¹ × 1/4) / ( 1/2)

5 Js⁻¹

Therefore, the at which the bar conducts now is 5 Js⁻¹

area of focus

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.