True or false: Everything in the universe works with harmony because of balanced energy
2 answers:
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Answer:
Explanation:
Given that, the range covered by the sphere, , when released by the robot from the height,
, with the horizontal speed
is
as shown in the figure.
The initial velocity in the vertical direction is .
Let be the acceleration due to gravity, which always acts vertically downwards, so, it will not change the horizontal direction of the speed, i.e.
will remain constant throughout the projectile motion.
So, if the time of flight is , then
Now, from the equation of motion
Where is the displacement is the direction of force,
is the initial velocity,
is the constant acceleration and
is time.
Here, and
(negative sign is for taking the sigh convention positive in
direction as shown in the figure.)
So, from equation (ii),
Similarly, for the launched height , the new time of flight,
, is
From equation (iii), we have
Now, the spheres may be launched at speed or
.
Let, the distance covered in the direction be
for
and
for
, we have
[from equation (iv)]
[from equation (i)]
(approximately)
This is in the points range as given in the figure.
Similarly,
[from equation (iv)]
[from equation (i)]
(approximately)
This is out of range, so there is no point for .
Hence, students must choose the speed to launch the sphere to get the maximum number of points.
Before answering this question, first we have to understand the effect of ratio of surface area to volume on the rate of diffusion.
The rate of diffusion for a body having larger surface area as compared to the ratio of surface area to volume will be more than a body having less surface area. Mathematically it can written as-
V∝ R [ where v is the rate of diffusion and r is the ratio of surface area to volume]
As per the question,the ratio of surface area to volume for a sphere is given
The surface area to volume ratio for right circular cylinder is given
Hence, it is obvious that the ratio is more for right circular cylinder.As the rate diffusion is directly proportional to the surface area to volume ratio,hence rate of diffusion will be more for right circular cylinder.
Hence the correct option is B. The rate of diffusion would be faster for the right cylinder.