1
IIT-JEE 2011 Paper 1 Offline
+3
-0.75

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

A
9
B
18
C
27
D
36
2
IIT-JEE 2010 Paper 1 Offline
+3
-0.75

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg(sinθ − μ cosθ) to P2 = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like

A
B
C
D
3
IIT-JEE 2009 Paper 2 Offline
+3
-1
A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration $$a$$. The distance of the new equilibrium position of the bead, where the bead can stays at rest with respect to the wire, from the y-axis is
A
$${a \over {gk}}$$
B
$${a \over {2gk}}$$
C
$${{2a} \over {gk}}$$
D
$${a \over {4gk}}$$
4
IIT-JEE 2009 Paper 1 Offline
+3
-1
A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $$\sqrt 3$$. The inclination θ of this inclined plane from the horizontal plane is gradually increased from $$0^\circ$$. Then
A
at θ = $$60^\circ$$, the block will start sliding down the plane
B
the block will remain at rest on the plane up to certain θ and then it will topple
C
at θ = $$60^\circ$$, the block will start sliding down the plane and continue to do so at higher angles
D
at θ = $$60^\circ$$, the block will start sliding down the plane and on further increasing θ, it will topple at certain θ
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