Answer:
Option B. 32 g
Explanation:
From the question given above, the following data were obtained:
Original amount (N₀) = 128 g
Half-life (t½) = 2.25 billion years
Number of half-lives (n) = 2
Amount remaining (N) =?
The amount of 128 gram of Radium-226 that will remain after 2 half-lives has elapsed can be obtained as followb
N = 1/2ⁿ × N₀
N = 1/2² × 128
N = 1/4 × 128
N = 0.25 × 128
N = 32 g
Therefore, 32g of the sample will remain.
The equilibrium temperature of aluminium and water is 33.2°C
We know that specific heat of aluminium is 0.9 J/gm-K, and that of water is 1 J/gm-K
Now we can calculate the equilibrium temperature
(mc∆T)_aluminium=(mc∆T)_water
15.7*0.9*(53.2-T)=32.5*1*(T-24.5)
T=33.2°C
Answer:
0.2932 rad/s
Explanation:
r = Radius = 2 m
= Initial angular momentum = 
= Initial angular velocity = 14 rev/min
= Final angular momentum
= Final angular velocity
Here the angular momentum of the system is conserved
The final angular velocity is 0.2932 rad/s
To calculate the initial velocity of the bike, we use the following equation
.
or
Here, u is initial velocity, v is final velocity, t is the time and d is the distance covered by bike.
Given, 
,
and 
.
Substituting these values in above equation, we get
.
Thus, the initial velocity of the bike is 1.2 m/s.
