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1. Two identical solid copper spheres of radius r placed in contact with each other. The gravitational attraction is proportional to : ?

2. Why 1.6 multiply 10 to the power -20 coulombs charge is not possible, where as 1.6 multiply 10 to the power -18 coulombs is possible

3. Clock a based on spring oscillations and a clock b based on oscillations of simple pendulum are synchronized on Earth. Both are taken to Mars. Where mass is 0.1 times mass of Earth and Radius is half of Earth's radius. What are the measures of time in both clocks now.

4. A soap solution has bubbles in it. The surface tension of that is S. Radius of a bubble is R and the pressure inside the bubble is atmospheric pressure. What is the electric potential on the surface of bubble?

5. An electric field of 30 n coulomb exists along the negative x axis in space. Calculate the potential difference Vb - Va where the points a and b are given by a=(0,0)and b(0,2)

6. If three infinite charged sheets of uniform surface charge densities of sigma ,2 sigma, - 4 sigma respectively are placed parallel to each other, Find electric field at different points.

7. Two conductors are of uniform shape and size one of them is made of copper, while the other is made of aluminum (less conductive). The charge induced in aluminum will be equal to copper or less or more ?

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1. F = G
M * M / x^2
distance x = 2 R = d = diameter
M =
(density p) * 4 pi /3 R^3 = 4 p
* pi /3 * d^3 /8
F = G M^2 / x^2
= G (p^2
pi^2/6^2) d^6 /d^2So F is
proportional to d^4Mass is dep. on diameter as density of the
material is a constant and Distance = diameter.
This happens only because they are in contact...
not in general...

============

2.
Electron charge e is the smallest
charge quantum possible. This is
established by quantum physics. Charge
exists in integral multiples of e. So q = 1.6
* 10^-20 coul is not possible.q = 1.6 * 10^-18
= 10 e ie., there are either 10
additional electrons or 10 electrons are taken away.

===========
3. Time
period T1 = 2 pi * root (m/k) for spring based clock a. time
period T2 = 2 pi * root(L/g) for clock b
based on pendulum.

g on Mars / g on Earth = ( M2 / R2^2 ) / (M1 /R1^2)
g' = 2 g

So T1' =
T1 remains same on Mars and Earth. T2'
= T2/root(2) ============

4.
Pressure difference between outside and inside of bubble =
P2 - P1 = 4 S / R

Force
exerted by this pressure difference on a small area on surface A
= F = 4 S / R * A

Let there
be an electric charge on the soap film.
Charge density = sigma

Electric field E at the surface =
sigma / (2 * epsilon_0) Electric Force on area A = E *
charge = sigma * (sigma * A) / (2 * epsilon). Electric force tries to explode the bubble.

Surface tension tries to contract the bubble. if the
bubble is in equilibrium => sigma^2
= 8 S epsilon / R

Electric potential V at the surface of bubble = q / (4 pi epsilon * R) q
= 4 pi R^2 * sigma V
= sigma
* R / epsilon = sqroot[8 S R/ epsilon ] ========== 5.
Electric field E is directed in the negative X direction. E points from b towards a. so
E = - E i Vb - Va
= E * distance = 2 E
Potential drops along the direction of E. ===============

6. Sheets
are S1, S2 and S3. S3 is negatively
charged. The field is directed away from
the sheet for S1 and S2. Field due to
S3 is directed towards S3.

The
magnitudes of the electric fields due to them respectively are:
E1 = sigma / (2 epsilon) = E
, say
E2 = 2 sigma / ( 2 epsilon) = 2 E
E3 = 4 sigma / (2 epsilon) = 4 E

Take a
point A on the left of all sheets. Point B between S1 and S2. Point C between S2 and S3. and point D is to the right of S3.

net
field E at A = - E1 - E2 + E3 = E
towards S3. net
field at B = E1 - E2 + E3 = 3 E towards
S3 net
field at C = E1 + E2 + E3 = 7 E
field at D = E1 + E2 - E3 = -
E towards S3.

===========

7. Copper
and Aluminum are good conductors. The Aluminum has more resistance than copper. But both conduct electricity well
enough.. When a charge is brought near
them, then equal and opposite charge is induced in either case... There is perhaps a little more energy is
spent to induce charges in Aluminum.
Electrons get either attracted or repelled towards the inducing
charge. Metals allow flow of electrons ,
so this property is needed. Resistance
causes heat generation. All metals will
have equal and opposite charge induced on them
during induction.