3. A car traveling at 40 m/s follows a curve in the road so that its centripetal

Question

3. A car traveling at 40 m/s follows a curve in the road so that its centripetal acceleration is 10 m/s. What is the radius of the curve? A) 4 m B) 8 m C) 80 m D) 160 m E) 640 m 4. A boy is whirling a stone around his head by means of a string. The string makes one complete revolution every second; and the magnitude of the tension in the string is F The boy then speeds up the stone, keeping the radius of the circle unchanged, so that the string makes two complete revolutions every second. What happens to the tension in the sting? A) The magnitude of the tension is unchanged. B) The magnitude of the tension reduces to half of its original value, F/2. C) The magnitude of the tension increases to twice its original value, 2F D) The magnitude of the tension increases to four times its original value, 4F E) The magnitude of the tension reduces to one-fourth of its original value, FI4. 5. A 0.25-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m. If the ball revolves four times every second, what is the tension in the string? A) 20 N///B) 8ON C) 60N D) 10N E) 20 N ust breaks when it is under 25 N of tension. A boy uses this string to whirl a 2-kg stone ina dish

Explanation / Answer

time period is T = (2*pi*r)/v

r is the radius of the circle

v is the speed of the stone

here r is constant

T1*v1 = T2*v2

1*v = 0.5*v2

v2 = 2*v

i.e now the stone was moving with the speed equal to twice the speed of the stone in earlier case

Tension = centripetal force = m*v^2/r

F1/v1^2 = F2/v2^2

F/v^2 = F2/(2v)^2

F2 = 4*F

hence the correct option is D)

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