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Pls somebody help me solve this ,you know it's really annoying me

Pls somebody help me solve this ,you know it's really annoying me 

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Grade:11

2 Answers

Mahek Raina
18 Points
4 years ago
We know, Hemispherical shell has centre of mass at a distance of R/2 from the plane surface.
Taking N as normal force at point of contact
Frictional coefficient u
And angle of inclination of inclined plane equal to A
Angle of friction as B
Angle theta as C
We know: tanB= u 
Draw the free body diagram 
Balancing the forces on the shell we get
N=mgcos(C-A)
un=mgsin(C-A) 
From above equations we find
tan(C-A) =u
Therefore C-A=B
A=C-B---------(I) 
For maximum theta or angle C we balance the moment
about Center of mass
N*(R*sin(C-B) /2) =uN*R(1-(cos(C-B))/2) 
sin(C-B) =tanB(2-cos(C-B)) 
Solving the above equation we get:
C=sin-1(2(sinB))
Theta=sin-1(2sin(lamda)) 
Vikas TU
14149 Points
4 years ago
Dear student 
Hope your doubt gets cleared 
Please refer the link below 
Good Luck 

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