Answer:
Part a)

Part b)

Part c)
Since we know that the base area will remain same always
so here the length and width of the object is not necessary to obtain the above data in such type of questions
Explanation:
Part a)
As we know that when cylinder float in the water then weight of the cylinder is counter balanced by the buoyancy force
So here we know
buoyancy force is given as



Now we know that the weight of the cylinder is given as

now we have


Part b)
When the same cylinder is floating in other liquid then we will have

so we have


Part c)
Since we know that the base area will remain same always
so here the length and width of the object is not necessary to obtain the above data in such type of questions
Answer:
Maximum spring length = 0.94m
Explanation:
Newton's law of forces in the vertical direction is given as:
Ef = Ks S - mg = 0
Ks = mg/ s
Ks = mg/ (L1 -Lo)
Ks =( 0.3 × 9.8 ) / ( 0.77 - 0.59 )
Ks = 2.94 / 0.18
Ks = 16.33N/m
The initial state is one in which the mass is pulled down so that the length of spring is 0.84m and the mass has initial speed of 1.8m/s. The final state is that in which the minimum point reached and the maximum length attained is L3
Ei = Ef
1/2mVi^2 + 1/2 Ks(L2-Lo)^2 + mg(L3- L2) = 1/2Ks(L3 - Lo)^2.
1/2 Mvi + 1/2 Ks(L2 - Lo)^2 + mg(L3 - L2)^2 = 1/2Ks(L3^2 - 2LoL3 + Lo^2)
1/2 KsL3 - (mg + KsLo)L3 + [1/2KsLo^2 + mgL2 - 1/2Ks(L2 -Lo)^2- 1/2mVi^2] = 0
Substituting the values to solve for L3 using the quadratic formula
1/2(16.33)L3^2 - (0.3×9.8) + 16.33(0.59)L3 + 1/2(16.33×0.59^2) + (0.3×9.8×0.84)- 1/2(16.33(0.84-0.59)^3 - 1/2( 0.3× 1.8^2] = 0
8.165L3^2 - 2.94 + 9.63L3 + 2.84 + 2.47 - 0.51 - 0.486
8.165L3^2 + 9.63L3 + 1.37
L3 =[ 9.63 +- sqrt(9.63^2 - 4(8.165)(1.37) / (2× 8.165)]
L3 =[ 9.63 +- sqrt(92.74 - 44.74) /16.33]
L3 = 9.63 +- sqrt(47.996)/16.43
L3 = 9.63 +- 6.93/ 16.33
L3 = (9.63 - 6.93)/16.34
L3 = 2.7/16.33
L3 = 0.165 + 0.77
L3= 0.935m
Gravity is greater when there is more mass and less distance between two objects
<span><span><span> m1m2
g = G---------
r</span></span></span>²
<span><span><span>
Where G gravitational constant, m1 and m2 the two masses, and r the distance between their centers. This shows that as either mass increases, the gravitational force increases; or as the distance increases, the gravitational force decreases exponentially. T
</span></span></span><span><span><span>
</span></span></span>
Temperature decreases and the atmosphere gets thiner.