Alan

Yes, R is not proportional to L, which measures the length of the cylinder, because the current flows radially.

.

Just 2 (equal to 91 that is).

.

This question only makes sense if the first row of Pascal's triangle is taken to be   1  1  (the first row is often given as just the number 1 on its own).  Given this then the sum of numbers in row n is 2ⁿ and there are n+1 numbers so the arithmetic mean is 2ⁿ/(n+1).  This equals 2048 when n = 15.

.

@ xvxvxv

 R is not proportional to the length L of the cylinder in this problem.

Also, if you are going to differentiate R with respect to A in your expression you are best to change the A from the denominator to A^-1 in the numerator.

.

Use energy = mass*specificheat capacity*temperature rise:

Assume density of water = 1000kg/m³, specific heat capacity of water = 4184 J/(kg.degC)

energy = 30*10^-6m³*1000kg/m³*4184J/(kg.degC)*(27-22)degC = 627.6 J

1 J is about 0.2389 calories  so energy = 627.6*0.2389 ≈ 150 calories  (Note these are not food calories.  1 food calorie is 1000 small calories)

.

.

Axially through simply refers to a situation in which the current is flowing in the direction of the long red arrow (see diagram below).  Radially outward refers to a situation in which the current is flowing in the direction of the short blue arrow.

The direction current flows will be determined by the potential difference in a particular case.  If there is a potential difference between the ends then current will flow axially; if there is a potential difference between an inner and an outer curved surface (as in the original problem) then current will flow radially.

.

F = G*m1*m2/r², where F is force, G is gravitational constant(6.673×10⁻¹¹ N·(m/kg)²), m's are masses and r is distance between masses.

$${\mathtt{1.27}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{8}}} = {\frac{{\mathtt{6.673}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\mathtt{m}}}{{{\mathtt{5}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{m}} = {\frac{{\mathtt{105\,151\,356\,211\,599}}}{{\mathtt{1\,105\,000\,000\,000}}}} \Rightarrow {\mathtt{m}} = {\mathtt{95.159\: \!598\: \!381\: \!537\: \!556\: \!6}}$$

The other mass is approximately 95 kg

.

c. The distance of each ball from the Earth's center of mass is almost identical.

.

a.  0 J

.