Answer:
d) The 2 athletes reach the same height, because the athletes run with the same speed.
Explanation:
In the whole process , kinetic energy is converted into potential energy .
1/2 m v² = mgh
v² = 2gh
h = v² / 2g
In this expression we see that height attained does not depend upon mass of the object . At the same time it also makes it clear that it depends upon velocity . As the velocity in both the cases are same , height attained by both of them will be same. Hence option d ) is correct.
Answer:
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Part 1
![V=1.57 \ \mu m^3](https://tex.z-dn.net/?f=V%3D1.57%20%5C%20%5Cmu%20m%5E3)
Part 2
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Explanation:
Given that
Diameter,d=1 μm
Length ,l=2 μm
As we know that volume of cylinder given as
![V=\pi r^2l](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2l)
![V=\pi \times 0.5^2\times 2 \ \mu m^3](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Ctimes%200.5%5E2%5Ctimes%202%20%5C%20%5Cmu%20m%5E3)
![V=1.57 \ \mu m^3](https://tex.z-dn.net/?f=V%3D1.57%20%5C%20%5Cmu%20m%5E3)
Surface area,A
A=π d l
![A=\pi \times 1 \times 2\ \mu m^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20%5Ctimes%201%20%5Ctimes%202%5C%20%5Cmu%20m%5E2)
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Part 1
![V=1.57 \ \mu m^3](https://tex.z-dn.net/?f=V%3D1.57%20%5C%20%5Cmu%20m%5E3)
Part 2
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Answer:
![\frac{\Delta L}{L} =5.37\times 10^{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20L%7D%7BL%7D%20%3D5.37%5Ctimes%2010%5E%7B-4%7D)
Explanation:
Given:
- cross sectional area of the wire,
![A=5.75\times 10^{-6}\ m^2](https://tex.z-dn.net/?f=A%3D5.75%5Ctimes%2010%5E%7B-6%7D%5C%20m%5E2)
- density of aluminium wire,
![\rho=2.7\times 10^3\ kg.m^{-3}](https://tex.z-dn.net/?f=%5Crho%3D2.7%5Ctimes%2010%5E3%5C%20kg.m%5E%7B-3%7D)
- young's modulus of the material,
![E=7\times 10^{10}\ N.m^{-2}](https://tex.z-dn.net/?f=E%3D7%5Ctimes%2010%5E%7B10%7D%5C%20N.m%5E%7B-2%7D)
- wave speed,
![v=118\ m.s^{-1}](https://tex.z-dn.net/?f=v%3D118%5C%20m.s%5E%7B-1%7D)
<u>We have mathematical expression for strain as:</u>
...............................(1)
and since, ![\sigma =\frac{T}{A}](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Cfrac%7BT%7D%7BA%7D)
where, T = tension force in the wire
equation (1) becomes:
............................(2)
<u>Also velocity ofwave in tensed wire:</u>
...................................(3)
where:
linear mass density of the wire
![\therefore \mu=\rho \times A](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cmu%3D%5Crho%20%5Ctimes%20A)
Now, equation (3) becomes
![v=\sqrt{\frac{T}{\rho \times A} }](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Crho%20%5Ctimes%20A%7D%20%7D)
............................(4)
Using eq. (2) & (4) for tension T
![v^2.\rho \times A=A.E\times \frac{\Delta L}{L}](https://tex.z-dn.net/?f=v%5E2.%5Crho%20%5Ctimes%20A%3DA.E%5Ctimes%20%5Cfrac%7B%5CDelta%20L%7D%7BL%7D)
![\frac{\Delta L}{L} =\frac{v^2.\rho}{E}](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20L%7D%7BL%7D%20%3D%5Cfrac%7Bv%5E2.%5Crho%7D%7BE%7D)
putting the respective values
![\frac{\Delta L}{L} =\frac{118^2\times 2.7\times 10^3}{7\times 10^{10}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20L%7D%7BL%7D%20%3D%5Cfrac%7B118%5E2%5Ctimes%202.7%5Ctimes%2010%5E3%7D%7B7%5Ctimes%2010%5E%7B10%7D%7D)
![\frac{\Delta L}{L} =5.37\times 10^{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20L%7D%7BL%7D%20%3D5.37%5Ctimes%2010%5E%7B-4%7D)
Answer:
The velocity of charge is 1.1×10⁴
Option(D)
Explanation:
F = q(v×B)
3.5×10-²= (8.4×10-⁴)*(v)*(6.7×10-³)*sin35
v = (3.5)/(8.4×6.7×0.57) × 10⁵
v = 3.5/32.08 × 10⁵
v = 0.109 × 10⁵
v ≈ 1.1 × 10⁴ m/s
Answer:
A crab lives in the intertidal zone.
A crab spends most of its time scavenging for food in the sand.
Explanation:
These tell us where a crab lives and where/how it feeds.
"A crab has an exoskeleton." is a true statement about the characteristics of a crab, but tells us nothing of its interaction with the environment so is not niche.
"A crab will avoid predators by quickly moving underneath an object to hide."
is a true statement, but is too general to identify a niche. Could be modified to cover niche if it said something like "A crab will avoid predators by quickly moving underneath an abandoned seashell or a coral rock to hide."