Answer:
128.21 m
Explanation:
The following data were obtained from the question:
Initial temperature (θ₁) = 4 °C
Final temperature (θ₂) = 43 °C
Change in length (ΔL) = 8.5 cm
Coefficient of linear expansion (α) = 17×10¯⁶ K¯¹)
Original length (L₁) =.?
The original length can be obtained as follow:
α = ΔL / L₁(θ₂ – θ₁)
17×10¯⁶ = 8.5 / L₁(43 – 4)
17×10¯⁶ = 8.5 / L₁(39)
17×10¯⁶ = 8.5 / 39L₁
Cross multiply
17×10¯⁶ × 39L₁ = 8.5
6.63×10¯⁴ L₁ = 8.5
Divide both side by 6.63×10¯⁴
L₁ = 8.5 / 6.63×10¯⁴
L₁ = 12820.51 cm
Finally, we shall convert 12820.51 cm to metre (m). This can be obtained as follow:
100 cm = 1 m
Therefore,
12820.51 cm = 12820.51 cm × 1 m / 100 cm
12820.51 cm = 128.21 m
Thus, the original length of the wire is 128.21 m
Answer:
Resultant force, R = 10 N
Explanation:
It is given that,
Force acting along +x direction, ![F_x=8\ N](https://tex.z-dn.net/?f=F_x%3D8%5C%20N)
Force acting along +y direction, ![F_y=6\ N](https://tex.z-dn.net/?f=F_y%3D6%5C%20N)
Both the forces are acting on a point object located at the origin. Let the resultant force of the object is given by R. So,
![R=\sqrt{F_x^2+F_y^2+F_xF_y\ cos\theta}](https://tex.z-dn.net/?f=R%3D%5Csqrt%7BF_x%5E2%2BF_y%5E2%2BF_xF_y%5C%20cos%5Ctheta%7D)
Here ![\theta=90^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D90%5E%7B%5Ccirc%7D)
![R=\sqrt{F_x^2+F_y^2}](https://tex.z-dn.net/?f=R%3D%5Csqrt%7BF_x%5E2%2BF_y%5E2%7D)
![R=\sqrt{8^2+6^2}](https://tex.z-dn.net/?f=R%3D%5Csqrt%7B8%5E2%2B6%5E2%7D)
R = 10 N
So, the resultant force on the object is 10 N. Hence, this is the required solution.
Objects will accelerate more by 10 (m/s)2
Answer:
B. A repulsive force of 8.0*10^3 N.
Explanation:
As we know by Coulomb's law that the electrostatic force between two charges is given as
![F = \frac{kq_1q_2}{r^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bkq_1q_2%7D%7Br%5E2%7D)
here we know that
![q_1 = -2 \times 10^2 C](https://tex.z-dn.net/?f=q_1%20%3D%20-2%20%5Ctimes%2010%5E2%20C)
![q_2 = -4 \times 10^{-8} C](https://tex.z-dn.net/?f=q_2%20%3D%20-4%20%5Ctimes%2010%5E%7B-8%7D%20C)
r = 3.0 m
now we have
![F = \frac{(9 \times 10^9)(2 \times 10^2)(4\times 10^{-8})}{3^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%289%20%5Ctimes%2010%5E9%29%282%20%5Ctimes%2010%5E2%29%284%5Ctimes%2010%5E%7B-8%7D%29%7D%7B3%5E2%7D)
![F = 8000 N](https://tex.z-dn.net/?f=F%20%3D%208000%20N)
since both charges are similar charges so they will repel each other by the force we calculated above so correct answer will be
B. A repulsive force of 8.0*10^3 N.