Answer:
<em>The rebound speed of the mass 2m is v/2</em>
Explanation:
I will designate the two masses as body A and body B.
mass of body A = m
mass of body B = 2m
velocity of body A = v
velocity of body B = -v since they both move in opposite direction
final speed of mass A = 2v
final speed of body B = ?
The equation of conservation of momentum for this system is
mv - 2mv = -2mv + x
where x is the final momentum of the mass B
x = mv - 2mv + 2mv
x = mv
to get the speed, we divide the momentum by the mass of mass B
x/2m = v = mv/2m
speed of mass B = <em>v/2</em>
Answer:
Option D. 23.5 m
Explanation:
From the question given above, the following data were obtained:
Frequency = 200 Hz
Speed of sound in brass = 4700 m/s
Wavelength of sound in brass =?
We can obtain the wavelength of the sound in the brass by using the following formula as illustrated below:
Wave speed = wavelength × frequency
4700 = wavelength × 200
Divide both side by 200
Wavelength = 4700 / 200
Wavelength = 23.5 m
Thus, the wavelength of the sound in the brass is 23.5 m
Answer:
the time rate of change of an object is directly proportional to the force acting on it unless an external force act on it to change it states of motion and takes the direction of the force
Answer:
(a) Ratio of mean density is 0.735
(b) Value of g on mars 0.920 ![m,/sec^2](https://tex.z-dn.net/?f=m%2C%2Fsec%5E2)
(c) Escape velocity on earth is ![3.563\times 10^4m/sec](https://tex.z-dn.net/?f=3.563%5Ctimes%2010%5E4m%2Fsec)
Explanation:
We have given radius of mars
and radius of earth ![R_{E}=1.3\times 10^4km=1.3\times 10^7m](https://tex.z-dn.net/?f=R_%7BE%7D%3D1.3%5Ctimes%2010%5E4km%3D1.3%5Ctimes%2010%5E7m)
Mass of earth ![M_E=5.972\times 10^{24}kg](https://tex.z-dn.net/?f=M_E%3D5.972%5Ctimes%2010%5E%7B24%7Dkg)
So mass of mars ![M_m=5.972\times\times 0.11 \times 10^{24}=0.657\times 10^{24}kg](https://tex.z-dn.net/?f=M_m%3D5.972%5Ctimes%5Ctimes%200.11%20%5Ctimes%2010%5E%7B24%7D%3D0.657%5Ctimes%2010%5E%7B24%7Dkg)
Volume of mars ![V=\frac{4}{3}\pi R^3=\frac{4}{3}\times 3.14\times (6.9\times 10^6)^3=1375.357\times 10^{18}m^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%3D%5Cfrac%7B4%7D%7B3%7D%5Ctimes%203.14%5Ctimes%20%286.9%5Ctimes%2010%5E6%29%5E3%3D1375.357%5Ctimes%2010%5E%7B18%7Dm%5E3)
So density of mars ![d_{mars}=\frac{mass}{volume}=\frac{0.657\times 10^{24}}{1375.357\times 10^{18}}=477.69kg/m^3](https://tex.z-dn.net/?f=d_%7Bmars%7D%3D%5Cfrac%7Bmass%7D%7Bvolume%7D%3D%5Cfrac%7B0.657%5Ctimes%2010%5E%7B24%7D%7D%7B1375.357%5Ctimes%2010%5E%7B18%7D%7D%3D477.69kg%2Fm%5E3)
Volume of earth ![V=\frac{4}{3}\pi R^3=\frac{4}{3}\times 3.14\times (1.3\times 10^7)^3=9.198\times 10^{21}m^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%3D%5Cfrac%7B4%7D%7B3%7D%5Ctimes%203.14%5Ctimes%20%281.3%5Ctimes%2010%5E7%29%5E3%3D9.198%5Ctimes%2010%5E%7B21%7Dm%5E3)
So density of earth ![d_{E}=\frac{mass}{volume}=\frac{5.972\times 10^{24}}{9.198\times 10^{21}}=649.271kg/m^3](https://tex.z-dn.net/?f=d_%7BE%7D%3D%5Cfrac%7Bmass%7D%7Bvolume%7D%3D%5Cfrac%7B5.972%5Ctimes%2010%5E%7B24%7D%7D%7B9.198%5Ctimes%2010%5E%7B21%7D%7D%3D649.271kg%2Fm%5E3)
(A) So the ratio of mean density ![\frac{d_{mars}}{d_E}=\frac{477.69}{649.27}=0.735](https://tex.z-dn.net/?f=%5Cfrac%7Bd_%7Bmars%7D%7D%7Bd_E%7D%3D%5Cfrac%7B477.69%7D%7B649.27%7D%3D0.735)
(B) Value of g on mars
g is given by ![g=\frac{GM}{R^2}=\frac{6.67\times 10^{-11}\times0.657\times 10^{24}}{(6.9\times 10^6)^2}=0.920m/sec^2](https://tex.z-dn.net/?f=g%3D%5Cfrac%7BGM%7D%7BR%5E2%7D%3D%5Cfrac%7B6.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes0.657%5Ctimes%2010%5E%7B24%7D%7D%7B%286.9%5Ctimes%2010%5E6%29%5E2%7D%3D0.920m%2Fsec%5E2)
(c) Escape velocity is given by
![v=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2\times 6.67\times 10^{-11}\times 0.657\times 10^{24}}{6.9\times 10^6}}=3.563\times 10^4m/sec](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7B2GM%7D%7BR%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%5Ctimes%206.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes%200.657%5Ctimes%2010%5E%7B24%7D%7D%7B6.9%5Ctimes%2010%5E6%7D%7D%3D3.563%5Ctimes%2010%5E4m%2Fsec)
Explanation:
Mathematicians seek and use patterns[8][9] to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.[10] Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11]
Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences.