1
AIEEE 2005
+4
-1
The upper half of an inclined plane with inclination $$\phi$$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
A
$$2\,\cos \,\,\phi$$
B
$$2\,sin\,\,\phi$$
C
$$\,\tan \,\,\phi$$
D
$$2\,\tan \,\,\phi$$
2
AIEEE 2005
+4
-1
A body of mass $$m$$ is accelerated uniformly from rest to a speed $$v$$ in a time $$T.$$ The instantaneous power delivered to the body as a function of time is given by
A
$${{m{v^2}} \over {{T^2}}}.{t^2}$$
B
$${{m{v^2}} \over {{T^2}}}.t$$
C
$${1 \over 2}{{m{v^2}} \over {{T^2}}}.{t^2}$$
D
$${1 \over 2}{{m{v^2}} \over {{T^2}}}.t$$
3
AIEEE 2005
+4
-1
A spherical ball of mass $$20$$ $$kg$$ is stationary at the top of a hill of height $$100$$ $$m$$. It rolls down a smooth surface to the ground, then climbs up another hill of height $$30$$ $$m$$ and finally rolls down to a horizontal base at a height of $$20$$ $$m$$ above the ground. The velocity attained by the ball is
A
$$20$$ $$m/s$$
B
$$40$$ $$m/s$$
C
$$10\sqrt {30} \,\,\,m/s$$
D
$$10\,\,m/s$$
4
AIEEE 2004
+4
-1
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $$x$$ is proportional to
A
$$x$$
B
$${e^x}$$
C
$${x^2}$$
D
$${\log _e}x$$
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