Explanation:
acceleration = change in velocity / change in time
a = v2-v1
- - - - - -
t
V1 = 0 ( since she stopped)
V2 = 9 m/s
t =15s
a = 9 - 0
- - - -
15
= 0.6m/s^2
Yes. Kinetic energy is a form of mechanical energy and friction will turn that kinetic energy into heat.
Answer: ![0.0039\ A](https://tex.z-dn.net/?f=0.0039%5C%20A)
Explanation:
Given
Diameter of the rod ![d=2.54\ cm](https://tex.z-dn.net/?f=d%3D2.54%5C%20cm)
length of rod is ![l=20\ cm](https://tex.z-dn.net/?f=l%3D20%5C%20cm)
Resistivity of silicon is ![\rho=6.4\times 10^2\ \Omega-m](https://tex.z-dn.net/?f=%5Crho%3D6.4%5Ctimes%2010%5E2%5C%20%5COmega-m)
cross-section of the rod ![A](https://tex.z-dn.net/?f=A)
![\Rightarrow A=\dfrac{\pi d^2}{4}\\\\\Rightarrow A=\dfrac{3.142\times 2.54^2\times 10^{-4}}{4}\\\\\Rightarrow A=5.067\times 10^{-4}\ m^2](https://tex.z-dn.net/?f=%5CRightarrow%20A%3D%5Cdfrac%7B%5Cpi%20d%5E2%7D%7B4%7D%5C%5C%5C%5C%5CRightarrow%20A%3D%5Cdfrac%7B3.142%5Ctimes%202.54%5E2%5Ctimes%2010%5E%7B-4%7D%7D%7B4%7D%5C%5C%5C%5C%5CRightarrow%20A%3D5.067%5Ctimes%2010%5E%7B-4%7D%5C%20m%5E2)
Resistance of rod is R
![\Rightarrow R=\dfrac{\rho l}{A}](https://tex.z-dn.net/?f=%5CRightarrow%20R%3D%5Cdfrac%7B%5Crho%20l%7D%7BA%7D)
![\Rightarrow R=\dfrac{640\times 0.20}{5.067\times 10^{-4}}\\\\\Rightarrow R=25.26\times 10^4\ \Omega](https://tex.z-dn.net/?f=%5CRightarrow%20R%3D%5Cdfrac%7B640%5Ctimes%200.20%7D%7B5.067%5Ctimes%2010%5E%7B-4%7D%7D%5C%5C%5C%5C%5CRightarrow%20R%3D25.26%5Ctimes%2010%5E4%5C%20%5COmega)
Current is given by
![\Rightarrow I=\dfrac{V}{R}\\\\\Rightarrow I=\dfrac{1000}{25.26\times 10^4}\\\\\Rightarrow I=0.0039\ A](https://tex.z-dn.net/?f=%5CRightarrow%20I%3D%5Cdfrac%7BV%7D%7BR%7D%5C%5C%5C%5C%5CRightarrow%20I%3D%5Cdfrac%7B1000%7D%7B25.26%5Ctimes%2010%5E4%7D%5C%5C%5C%5C%5CRightarrow%20I%3D0.0039%5C%20A)
Explanation:
It is given that,
The volume of a right circular cylindrical, ![V=108\ cm^3](https://tex.z-dn.net/?f=V%3D108%5C%20cm%5E3)
We know that the volume of the cylinder is given by :
![V=\pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20h)
............(1)
The upper area is given by :
![A=32r^2+2\pi rh](https://tex.z-dn.net/?f=A%3D32r%5E2%2B2%5Cpi%20rh)
![A=32r^2+2\pi r\times \dfrac{108}{\pi r^2}](https://tex.z-dn.net/?f=A%3D32r%5E2%2B2%5Cpi%20r%5Ctimes%20%5Cdfrac%7B108%7D%7B%5Cpi%20r%5E2%7D)
![A=32r^2+\dfrac{216}{r}](https://tex.z-dn.net/?f=A%3D32r%5E2%2B%5Cdfrac%7B216%7D%7Br%7D)
For maximum area, differentiate above equation wrt r such that, we get :
![\dfrac{dA}{dr}=64r-\dfrac{216}{r^2}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdr%7D%3D64r-%5Cdfrac%7B216%7D%7Br%5E2%7D)
![64r-\dfrac{216}{r^2}=0](https://tex.z-dn.net/?f=64r-%5Cdfrac%7B216%7D%7Br%5E2%7D%3D0)
![r^3=\dfrac{216}{64}](https://tex.z-dn.net/?f=r%5E3%3D%5Cdfrac%7B216%7D%7B64%7D)
r = 1.83 m
Dividing equation (1) with r such that,
![\dfrac{h}{r}=\dfrac{108}{\pi r}](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%7D%7Br%7D%3D%5Cdfrac%7B108%7D%7B%5Cpi%20r%7D)
![\dfrac{h}{r}=\dfrac{108}{\pi 1.83}](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%7D%7Br%7D%3D%5Cdfrac%7B108%7D%7B%5Cpi%201.83%7D)
![\dfrac{h}{r}=59 \pi](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%7D%7Br%7D%3D59%20%5Cpi)
Hence, this is the required solution.
Answer:
False
Explanation:
The steel ball and the wooden ball do not have the same force acting on them because their masses are different. But, they have the same acceleration which is the acceleration due to gravity g = 9.8 m/s².
Using the equation of motion under freefall, s = ut +1/2gt². Since u = 0,
s = 1/2gt² ⇒ t = √(2s/g)
Since. s = height is the same for both objects, they land at the same time neglecting air resistance.