1
AIPMT 2003
MCQ (Single Correct Answer)
+4
-1
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. then the fraction of total energy associated with its rotational energy will be
A
$${{{K^2} + {R^2}} \over {{R^2}}}$$
B
$${{{K^2}} \over {{R^2}}}$$
C
$${{{K^2}} \over {{K^2} + {R^2}}}$$
D
$${{{R^2}} \over {{K^2} + {R^2}}}$$
2
AIPMT 2003
MCQ (Single Correct Answer)
+4
-1
A stone is tied to a string of length $$l$$ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is
A
$$\sqrt {2\left( {{\mu ^2} - gl} \right)} $$
B
$$\sqrt {{u^2} - gl} $$
C
$$u - \sqrt {{u^2} - 2gl} $$
D
$$\sqrt {2gl} $$
3
AIPMT 2003
MCQ (Single Correct Answer)
+4
-1
A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom ?
A
$$\sqrt {2gh} $$
B
$$\sqrt {{3 \over 4}gh} $$
C
$$\sqrt {{4 \over 3}gh} $$
D
$$\sqrt {4gh} $$
4
AIPMT 2003
MCQ (Single Correct Answer)
+4
-1
A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $$\omega $$. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be :
A
$${{M\omega } \over {4m}}$$
B
$${{M\omega } \over {M + 4m}}$$
C
$${{\left( {M + 4m} \right)\omega } \over M}$$
D
$${{\left( {M - 4m} \right)\omega } \over {M + 4m}}$$
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