Answer: ![-\frac{1}{2}\times \frac{d[Br^.]}{dt}=+\frac{d[Br_2]}{dt}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cfrac%7Bd%5BBr%5E.%5D%7D%7Bdt%7D%3D%2B%5Cfrac%7Bd%5BBr_2%5D%7D%7Bdt%7D)
Explanation:
Rate of a reaction is defined as the rate of change of concentration per unit time.
Thus for reaction:

The rate in terms of reactants is given as negative as the concentration of reactants is decreasing with time whereas the rate in terms of products is given as positive as the concentration of products is increasing with time.
![Rate=-\frac{d[Br^.]}{2dt}](https://tex.z-dn.net/?f=Rate%3D-%5Cfrac%7Bd%5BBr%5E.%5D%7D%7B2dt%7D)
or ![Rate=+\frac{d[Br_2]}{dt}](https://tex.z-dn.net/?f=Rate%3D%2B%5Cfrac%7Bd%5BBr_2%5D%7D%7Bdt%7D)
Thus ![-\frac{d[Br^.]}{2dt}=+\frac{d[Br_2]}{dt}](https://tex.z-dn.net/?f=-%5Cfrac%7Bd%5BBr%5E.%5D%7D%7B2dt%7D%3D%2B%5Cfrac%7Bd%5BBr_2%5D%7D%7Bdt%7D)
Answer:
KE = 1.75 J
Explanation:
given,
mass of ball, m₁ = 300 g = 0.3 Kg
mass of ball 2, m₂ = 600 g = 0.6 Kg
length of the rod = 40 cm = 0.4 m
Angular speed = 100 rpm= 
=10.47\ rad/s
now, finding the position of center of mass of the system
r₁ + r₂ = 0.4 m.....(1)
equating momentum about center of mass
m₁r₁ = m₂ r₂
0.3 x r₁ = 0.6 r₂
r₁ = 2 r₂
Putting value in equation 1
2 r₂ + r₂ = 0.4
r₂ = 0.4/3
r₁ = 0.8/3
now, calculation of rotational energy




KE = 1.75 J
the rotational kinetic energy is equal to 1.75 J
Answer:

Explanation:
We know that acceleration is change in velocity over time.


v is the final velocity and u is the initial velocity.
Solve for v.
Multiply both sides by t.

Add u to both sides.

Answer:twice of initial value
Explanation:
Given
spring compresses
distance for some initial speed
Suppose v is the initial speed and k be the spring constant
Applying conservation of energy
kinetic energy converted into spring Elastic potential energy

When speed doubles

divide 1 and 2


Therefore spring compresses twice the initial value