Answer:
Yes
Explanation:
If the acceleration has an opposite direction to the velocity of the car, this means that it is opposed to is motion. Therefore, it is called deceleration, since the car's velocity will decrease until it stops and then will start it moving towards the west.
Answer:
The smallest diameter is ![D =122 \ m](https://tex.z-dn.net/?f=D%20%3D122%20%5C%20m)
Explanation:
From the question we are told that
The resolution of the telescope is ![\theta = 0.00350 \ arc \ second](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%200.00350%20%5C%20arc%20%5C%20second)
The wavelength is ![\lambda = 1.70 \mu m = 1.70 *10^{-6} \ m](https://tex.z-dn.net/?f=%5Clambda%20%3D%201.70%20%5Cmu%20m%20%3D%201.70%20%2A10%5E%7B-6%7D%20%5C%20m)
From the question we are told that
![1 arc \ sec = \frac{1}{3600^o}](https://tex.z-dn.net/?f=1%20arc%20%5C%20sec%20%3D%20%5Cfrac%7B1%7D%7B3600%5Eo%7D)
So ![0.00350 \ arc \ second = x](https://tex.z-dn.net/?f=0.00350%20%5C%20arc%20%5C%20second%20%3D%20x)
Therefore
![x = 0.00350 * \frac{1}{3600 }](https://tex.z-dn.net/?f=x%20%3D%20%200.00350%20%20%2A%20%20%5Cfrac%7B1%7D%7B3600%20%7D)
![x = ( 9.722*10^{-7} )^o](https://tex.z-dn.net/?f=x%20%3D%20%28%209.722%2A10%5E%7B-7%7D%20%29%5Eo)
Now ![1^o = \frac{\pi}{180}](https://tex.z-dn.net/?f=1%5Eo%20%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B180%7D)
So ![(9.722*10^{-7})^o = \theta](https://tex.z-dn.net/?f=%289.722%2A10%5E%7B-7%7D%29%5Eo%20%3D%20%20%5Ctheta)
=> ![\theta = (9.722*10^{-7}) * \frac{\pi}{180}](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%20%289.722%2A10%5E%7B-7%7D%29%20%2A%20%5Cfrac%7B%5Cpi%7D%7B180%7D)
![\theta = 1.69*10^{-8} rad](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%201.69%2A10%5E%7B-8%7D%20rad)
The smallest diameter is mathematically represented as
![D = \frac{1.22 \lambda }{\theta }](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B1.22%20%5Clambda%20%7D%7B%5Ctheta%20%20%7D)
substituting values
![D = \frac{1.22 * 1.7 *10^{-6}} {1.69 *10^{-8} }](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B1.22%20%2A%201.7%20%2A10%5E%7B-6%7D%7D%20%7B1.69%20%2A10%5E%7B-8%7D%20%20%7D)
![D =122 \ m](https://tex.z-dn.net/?f=D%20%3D122%20%5C%20m)
Answer:
0 J
Explanation:
As work is force times displacement, if no displacement occurs, no work occurs.
Answer:
35%
Explanation:
The car's engine gives off 65% thermal energy
So only 35 % is converted into mechanical energy .
input heat = Q₁ = 100
output heat = Q₂ = 65
Work output = Q₁ - Q₂ = W
W = 100 - 65 = 35
Efficiency = W / Q₁ X 100
= (35/ 100) X 100
= 35%.
Answer:
Explanation:
Moment of inertia of a disc = 1/2 M R²
Since mass is same for both and radius are r and 2r, their moment of inertia can be in the ratio of 1: 4 . Let them be I and 4I . Angular speed are ω₀ and - ω₀ .
We shall apply law of conservation of angular momentum .
initial total angular momentum
I x ω₀ - 4I x ω₀ = - 3Iω₀
Let final common angular momentum be ω
total final angular momentum = ( I + 4I ) ω
Applying law of conservation of angular momentum
( I + 4I ) ω = - 3Iω₀
ω = - 3 / 5 ω₀ .
b )
Initial total rotational K E
= 1/2 I ω₀² + 1/2 4I ω₀²
= 1/2 x5I ω₀²
Final total rotational K E
= 1/2 ( I + 4I ) ( - 3 / 5 ω₀ )²
= 1/2 x 9 / 5 I ω₀²
= 9 / 10I ω₀²
change in rotational kinetic energy = 9 / 10I ω₀² - 1/2 x5I ω₀²
(9/10 - 5/2) xI ω₀²
=( .9 - 2.5 )I ω₀²
= - 1.6 I ω₀² Ans