A small particle of mass m is released from rest from point P inside a smooth hemispherical bowl as shown in figure. The normal reaction on the particle varies with theta as:-

Question

​A small particle of mass m is released from rest from point
P inside a smooth hemispherical bowl as shown in figure The normal
reaction on the particle varies with theta as:-

Vara · Accepted Answer

Dear Student,
Please find below the solution to the asked
query:

From the law of conservation of energy:Gain in KE=Loss in PE12mv2=mgh12mv2=mgRsinθv2=2gRsinθNet force along radial direction:Centripetal force=Normal force-Component of weightmv2R=N-mgsinθSubstitute v2=2gRsinθ in the above equation:m2gRsinθR=N-mgsinθN=3mg sinθFor θ=00, N=0For θ=900, N=3mgHence,the graph 2 gives correct relationship between normal reaction and angle

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​A small particle of mass m is released from rest from point P inside a smooth hemispherical bowl as shown in figure. The normal reaction on the particle varies with theta as:-

A small particle of mass m is released from rest from point P inside a smooth hemispherical bowl as shown in figure. The normal reaction on the particle varies with theta as:-