Explanation
By a load, when the metal wire is stretched, in the transverse length, the fractional change is proportional to the longitudinal length's fractional change.
Let the cross functional area be denoted as “A” and length is denoted as “l”. Wire's volume is shown as Al.
Let's assume that there is no lateral strain when there is an occurrence of longitudinal strain.
Volume increase can be shown as:
△V=A△l
△VV=A△lAl=△ll
So, △VV is directly proportional to △ll
Option (A) is correct.
When external force is applied, work done is given by
Work done W=mgΔx
And
W2=12×stress×strain×volume
12×Y×(strain)2×V
12×Y×(ΔxL)2×AL
YΔx2A2L
So, total work done is
W=mgΔx+YΔx2A2L
Given,
Radius of sphere, R
Mass placed on massless piston, M.
Area of piston, A
Change in pressure ΔP=ΔFA=Mg−0A=MgA
Volume of sphere, v=43πR3
Small decrease in volume, −dv=d(43πR3)=4πR2dR
Bulk modulus, B
B=dp−dvv=MgA−4πR2dR43πR3=Mg−3AdRR
−dRR=Mg3AB
Hence, fractional decrease in radius of sphere is Mg3AB
The weight of suspended mass is given as,
W1=mg
The weight of the rod acting at the midpoint is given as,
W2=mg2
The stress at the midpoint is given as,
σ=W1+W2A
σ=mg+mg2A
σ=3mg2A
A thick rope of rubber of density 1.5×103kg/m3 and Young's modulus 5×106N/m2 , 8m length is hung from the ceiling of a room , the increases in its length due to its own weight is :
(g=10m/s2)
A massless and thin string is wrapped several times around a disc kept on a rough horizontal surface. A boy standing at a distance 'd' for the cylinder holds free end of the string pulls the cylinder towards him. If there is no slipping, length of the string passed through the hand of the boy while the cylinder reaches his hands is
An elastic string carrying a body of mass 'm' extends by 'e'. The body rotates in a vertical circle with critical velocity. The extension in the string at the lowest position is
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