A car of mass 1000kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is 45∘, the speed of car is (Take g=10m/s2)
A
20ms−1
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B
30ms−1
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C
5ms−1
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D
10ms−1
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Solution
The correct option is B30ms−1
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=tan−1(v2rg) where, v = speed and r = radius For banking, tanθ=v2rg ⇒tan45∘=v290×10=1 ⇒v2=900 ⇒v=√900m/s=30m/s