Question 31 : A motor cyclist loops a vertical circular loop of diameter 18 m, without dropping down, even at the highest point of the loop. What should be his minimum speed at the lowest point of the loop?
1. 10 m/s
2. 21 m/s
3. 30 m/s
4. 16 m/s
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Question 32 : A mass suspended on a frictional less horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity w0. If length of the string and angular velocity are doubled the tension in the string which was initially T0 is now
1. 8 T0
2. T0/2
3. 4 T0
4. T0
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Question 33 : A metal sphere of mass 0.1 kg is attached to an inextensible string of length 130 cm whose upper end is fixed to the rigid support. If the sphere is made to describe a horizontal circle of radius 50 cm, the time for its one revolution is near about
1. 1.2 sec
2. 3 sec
3. 1.5 sec
4. 2.2 sec
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Question 34 : A fighter aeroplane flying in the sky dives with a speed of 360 km/hr in a vertical circle of radius 200 m. Weight of the pilot sitting in it is 75 kg. What will be the value of force with which the pilot presses his seat when the aeroplane is at highest position (g = 10 m/s2)
1. 1500 N
2. 3000 N
3. 300 N
4. (75 ' g)N
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Question 35 : A man whirls a stone of mass 250 gram, tied at the end of a string of length 2 m in a horizontal circle and at a height of 5 m from the ground. The string breaks and the stone flies off tangenitially and strikes the ground at a horizontal distance of 10 m from the man. What was the magnitude of the centripetal acceleration of the stone, when it was moving in the circle? (g = 10 m/s2)
1. 50 m/s²
2. 25 m/s²
3. 40 m/s²
4. 30 m/s²
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Question 36 : A mass of 5 kg is tied to a string of length 1.0 m and is rotated in vertical circle with a uniform speed of 4 m/s. The tension in the string will be 130 N when the mass is at (g = 10 m/s²)
1. highest point
2. mid way
3. bottom
4. cannot be justified
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Question 37 : A cyclist goes round a circular path of circumference 343 m in s. The angle made by him, with the vertical is
1. 42°
2. 43°
3. 44°
4. 45°
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Question 38 : A frictional track ABCDE ends in a circular loop of radius R, body slides down the track from point A which is at a height h of 5 cm. Maximum value of R for the body to successfully complete the loop is:
1. 5 cm
2. 10/3 cm
3. 2 cm
4. 15/4 cm
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Question 39 : A cyclist turns around a curve at 15 miles per hour. If he turns at double the speed, the tendency of overturn is
1. quadrupled
2. halved
3. unchanged
4. doubled
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Question 40 : A cyclist is moving in a circular track of radius 80 m, with a velocity of 36 km/hour. In order to keep his balance, he has to lean inwards from the vertical through an angle q. If g = 10 m/s2, then q is given by
1. tan^-1 (2)
2. tan^-1 (4)
3. tan^-1 (1/4)
4. tan^-1 (1/8)
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