Answer:

Explanation:
From the given information:
The elastic potential energy can be calculated by using the formula:

Making K the subject;


k = 2.3 × 10⁻² N/m
Now; the frequency of the small oscillation can be determined by using the formula:

where;
m = mass of each atom = 1.66 × 10⁻²⁶ kg


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Answer:
The shear modulus of the polymer is 5 MPa
Solution:
As per the question:
displacement of the top plate, d = 2 mm = 0.002 m
Horizontal Force, P = 2 kN = 2000 N
Width of the block, w = 100 mm = 0.1 m
By small angle analysis:
Angle, 
Now,
Stress,
= 

Answer:
Electric field, E = 
Explanation:
Given that,
The potential difference across the membrane, 
The thickness of the membrane is, 
We need to find the magnitude of the electric field in the membrane. We know that the relation between electric field and electric potential is given by :

So, the magnitude of the electric field in the membrane is
.
Answer:
(a). The frequency of this standing wave is 0.782 kHz.
(b). The frequency of the fundamental standing wave in the air is 1.563 kHz.
Explanation:
Given that,
Length of tube = 11.0 cm
(a). We need to calculate the frequency of this standing wave
Using formula of fundamental frequency

Put the value into the formula



(b). If the test tube is half filled with water
When the tube is half filled the effective length of the tube is halved
We need to calculate the frequency
Using formula of fundamental frequency of the fundamental standing wave in the air

Put the value into the formula



Hence, (a). The frequency of this standing wave is 0.782 kHz.
(b). The frequency of the fundamental standing wave in the air is 1.563 kHz.