The gravitational force <em>F</em> between two masses <em>M</em> and <em>m</em> a distance <em>r</em> apart is
<em>F</em> = <em>G M m</em> / <em>r</em> ²
Decrease the distance by a factor of 7 by replacing <em>r</em> with <em>r</em> / 7, and decrease both masses by a factor of 8 by replacing <em>M</em> and <em>m</em> with <em>M</em> / 8 and <em>m</em> / 8, respectively. Then the new force <em>F*</em> is
<em>F*</em> = <em>G </em>(<em>M</em> / 8) (<em>m</em> / 8) / (<em>r</em> / 7)²
<em>F*</em> = (1/64 × <em>G M m</em>) / (1/49 × <em>r</em> ²)
<em>F*</em> = 49/64 × <em>G M m</em> / <em>r</em> ²
In other words, the new force is scaled down by a factor of 49/64 ≈ 0.7656, so the new force has magnitude approx. 76.56 N.
The law of conservation of energy implies that energy can neither be created nor destroyed, but can be changed from one form to another.
Answer:
5. -24 m/s²
Explanation:
Acceleration: This can be defined as the rate of change of velocity.
The S.I unit of acceleration is m/s².
mathematically,
a = dv/dt ............................ Equation 1
Where a = acceleration, dv/dt = is the differentiation of velocity with respect to time.
But
v = dx(t)/dt
Where,
x(t) = 27t-4.0t³...................... Equation 2
Therefore, differentiating equation 2 with respect to time.
v = dx(t)/dt = 27-12t²............. Equation 3.
Also differentiating equation 3 with respect to time,
a = dv/dt = -24t
a = -24t .................... Equation 4
from the question,
At the end of 1.0 s,
a = -24(1)
a = -24 m/s².
Thus the acceleration = -24 m/s²
The right option is 5. -24 m/s²
Intensity of sunlight at given position is defined as power received per unit area
so here we can say

area on which photons are received is given as

now we can find the power received due to sunlight



now we can say this power is due to photons that strikes on surface of earth
so here we can say

given here that





so it will strike 2.47 * 10^18 photons on given area per second
Answer:
65.73N
Explanation:
The frictional force is a force that opposes the motion of an object on a flat surface or an inclined surface.
It is always acting up an incline plane .
Since the pipe will tend to roll up the plane, then both the impending force P also known as frictional force and the moving force Fm both will be acting up the plane.
The net force acting up the plane is
Fnet = P + Fm... (1)
The force perpendicular to the plane known as the normal reaction R must be equal to the force acting along the ramp in other to keep the body in equilibrium i.e R = Fnet
If R = W = mgcos (theta)
and Fm = mgsin(theta)
Then mgcos theta = Fnet
mgcos (theta) = P+Fm
mgcos (theta) = P+mgsin(theta)
P = mgcos (theta) - mgsin(theta)... (2)
Given mass = 10kg
g = 9.81m/s
We can get theta from the formula;
µ = Ff/R = wsin theta/wcos theta
µ = sin theta/cos theta
µ = tan(theta)
0.3 = tan (theta)
theta = arctan0.3
theta = 16.7°
P = 10(9.81)cos16.7° - 10(9.81)sin16.7°
P = 98.1(cos16.7°-sin16.7°)
P = 98.1(0.67)
P = 65.73N
The minimum force P required to cause impending motion is 65.73N