Answer:v=3.28 m/s
Explanation:
Given
mass of rock ![m=500 gm](https://tex.z-dn.net/?f=m%3D500%20gm)
diameter of circle ![d=2.2 m](https://tex.z-dn.net/?f=d%3D2.2%20m)
radius ![r=\frac{2.2}{2}=1.1 m](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2.2%7D%7B2%7D%3D1.1%20m)
At highest Point
![mg+N=\frac{mv^2}{r}](https://tex.z-dn.net/?f=mg%2BN%3D%5Cfrac%7Bmv%5E2%7D%7Br%7D)
At highest Point N=0 because mass is just balanced by centripetal Force
thus ![mg=\frac{mv^2}{r}](https://tex.z-dn.net/?f=mg%3D%5Cfrac%7Bmv%5E2%7D%7Br%7D)
![v=\sqrt{gr}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7Bgr%7D)
![v=\sqrt{9.8\times 1.1}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B9.8%5Ctimes%201.1%7D)
![v=\sqrt{10.78}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B10.78%7D)
![v=3.28 m/s](https://tex.z-dn.net/?f=v%3D3.28%20m%2Fs)
Answer:
m = 3.91 kg
Explanation:
Given that,
Mass of the object, m = 3.74 kg
Stretching in the spring, x = 0.0161 m
The frequency of vibration, f = 3.84 Hz
When the object is suspended, the gravitational force is balanced by the spring force as :
![mg=kx](https://tex.z-dn.net/?f=mg%3Dkx)
![k=\dfrac{mg}{x}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7Bmg%7D%7Bx%7D)
![k=\dfrac{3.74\times 9.8}{0.0161}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B3.74%5Ctimes%209.8%7D%7B0.0161%7D)
k = 2276.52 N/m
The frequency of vibration is given by :
![f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}](https://tex.z-dn.net/?f=f%3D%5Cdfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D)
![m=\dfrac{k}{4\pi^2f^2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bk%7D%7B4%5Cpi%5E2f%5E2%7D)
![m=\dfrac{2276.52}{4\pi^2\times (3.84)^2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B2276.52%7D%7B4%5Cpi%5E2%5Ctimes%20%283.84%29%5E2%7D)
m = 3.91 kg
So, the mass of the object is 3.91 kg. Hence, this is the required solution.
Answer:
![q = \dfrac{14}{100}](https://tex.z-dn.net/?f=q%20%3D%20%5Cdfrac%7B14%7D%7B100%7D)
Explanation:
given,
86 out of every 100 TV households have at least one remote control
Probability of any material is calculated by.
![Probability = \dfrac{favourable\ outcome}{Total\ outcome}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cdfrac%7Bfavourable%5C%20outcome%7D%7BTotal%5C%20outcome%7D)
![P(at\ least\ one\ remote\ control)=\dfrac{86}{100}](https://tex.z-dn.net/?f=P%28at%5C%20least%5C%20one%5C%20remote%5C%20control%29%3D%5Cdfrac%7B86%7D%7B100%7D)
![P(at\ least\ one\ remote\ control)=0.86](https://tex.z-dn.net/?f=P%28at%5C%20least%5C%20one%5C%20remote%5C%20control%29%3D0.86)
now, Calculating probability that at least one remote control
q = 1 - 0.86
q = 0.14
![P(doesnot\ have\ at\ least\ one\ remote\ control)=\dfrac{14}{100}](https://tex.z-dn.net/?f=P%28doesnot%5C%20have%5C%20at%5C%20least%5C%20one%5C%20remote%5C%20control%29%3D%5Cdfrac%7B14%7D%7B100%7D)
![q = \dfrac{14}{100}](https://tex.z-dn.net/?f=q%20%3D%20%5Cdfrac%7B14%7D%7B100%7D)