Answer: the water level would rise since the pebble displaces minimal water compared to the boat.
Explanation:..........
 
        
             
        
        
        
Answer:
 time taken is equal to 14,156 years
Explanation:
we know,

at t = 0 
Y(0) = A
given that half life of plutonium 239 = 24,200



hence time taken is equal to 14,156 years
 
        
             
        
        
        
Answer:
Explanation:
Given
Original Frequency 
apparent Frequency 
There is change in frequency whenever source move relative to the observer.
From Doppler effect we can write as 

where  
 apparent frequency
apparent frequency  
v=velocity of sound in the given media
 velocity of source
velocity of source
 velocity of observer
velocity of observer   
here 




i.e.fork acquired a velocity of 
distance traveled by fork is given by

where v=final velocity
u=initial velocity
a=acceleration
s=displacement



                                        
 
        
             
        
        
        
Answer:
487.23 N/m
Explanation:
Given:
mass of metal sphere 'm'= 0.51kg
the spring stretches from 0.12 m to 0.23 m. Therefore,
 = 0.12m and
= 0.12m and  = 0.23m
= 0.23m
the speed of the sphere decreases from 6.7 to 3.3 m/s. Therefore,
 = 6.7m/s and
= 6.7m/s and  =3.3m/s
=3.3m/s
In order to find spring constant, we apply law of conservation of energy. i.e
The change of the kinetic energy of sphere is equal to the change of potential energy of the spring.
So, Δ Δ
 Δ
where, 
Δ 1/2 m (
 1/2 m ( -
-  )²
)²
Δ = 1/2 k (
= 1/2 k ( -
 -  )²
)²
1/2 m ( -
-  )² = 1/2 k (
)² = 1/2 k ( -
-  )²
 )²
k= m [ ( -
-  )²/(
)²/( -
-  )²
 )²
k= 0.51 [(6.7-3.3)²/ (0.23-0.12)²]
k= 487.23 N/m 
Thus, the spring constant of the spring is 487.23 N/m