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Question

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45, the speed of car is (Take g=10 m/s2)

A
20ms1
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B
30ms1
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C
5ms1
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D
10ms1
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Solution

The correct option is B 30ms1

By the free body diagram and writing the force equation we get,
Ncosθ=mg ...(i)
Nsinθ=mv2r ...(ii)
Now by dividing both the above equations, we get,
θ=tan1(v2rg)
where, v = speed and r = radius
For banking, tanθ=v2rg
tan45=v290×10=1
v2=900
v=900 m/s=30 m/s

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