1

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is ${2 \over 3}$ times the wavelength in free space. The radius of the curved surface of the lens is
A
1 m
B
2 m
C
3 m
D
6 m
2

IIT-JEE 2011

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
3

IIT-JEE 2010

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 4

IIT-JEE 2009

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