Feelings of jealousy and envy
Answer:
Explanation:
λ=c x²
c = λ / x²
λ is mass / length
so its dimensional formula is ML⁻¹
x is length so its dimensional formula is L
c = λ / x²
= ML⁻¹ / L²
= ML⁻³
B )
We shall find out the mass of the rod with the help of given expression of mass per unit length and equate it with given mass that is M
The mass in the rod is symmetrically distributed on both side of middle point.
we consider a small strip of rod of length dx at x distance away from middle point
its mass dm = λdx = cx² dx
By integrating it from -L to +L we can calculate mass of whole rod , that is
M = ∫cx² dx
= [c x³ / 3] from -L/2 to +L/2
= c/3 [ L³/8 + L³/8]
M = c L³/12
c = 12 M L⁻³
C ) Moment of inertia of rod
∫dmx²
= ∫λdxx²
= ∫cx²dxx²
= ∫cx⁴dx
= c x⁵ / 5 from - L/2 to L/2
= c / 5 ( L⁵/ 32 +L⁵/ 32)
= (2c / 160)L⁵
= (c / 80) L⁵
= (12 M L⁻³/80)L⁵
= 3/20 ML²
=
=
Answer:
(E) none of these.
Explanation:
first that all we need the meaning of a Watt
<em>" is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 </em><em>joule</em><em> per </em><em>second</em><em>,[1] and is used to quantify the rate of </em><em>energy</em><em> transfer." </em>
<em>definition taken from wikipedia.org</em>
now with this concept we have that:
100 W means 100 J/s .Therefore it uses 100 J energy per second
therefore on the answers don't mention this three terms together
Joules, energy and second so the answer must be.
(E) None of these
Answer: -4.4 m/s
Explanation:
This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum 
must be equal to the final momentum 
:
(1)
Where:
(2)
(3)
is the mass of the child
is the initial velocity of the child
is the mass of the adult
is the initial velocity of the adult (it is sitting still)
is the final velocity of the child
is the final velocity of the adult
Substituting (2) and (3) in (1):
(4)
Isolating :
(5)
(6)
Finally:
This means the velocity of the child is in the opposite direction
