1
IIT-JEE 2008 Paper 2 Offline
+3
-1

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.

The centre of mass of the disk undergoes simple harmonic motion with angular frequency $$\omega$$ equal to:

A
$$\sqrt {{k \over M}}$$
B
$$\sqrt {{{2k} \over M}}$$
C
$$\sqrt {{{2k} \over {3M}}}$$
D
$$\sqrt {{{4k} \over {3M}}}$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.

The maximum value of V$$_0$$ for which the disk will roll without slipping is:

A
$$\mu g\sqrt {{M \over k}}$$
B
$$\mu g\sqrt {{M \over {2k}}}$$
C
$$\mu g\sqrt {{{3M} \over k}}$$
D
$$\mu g\sqrt {{{5M} \over {2k}}}$$
3
IIT-JEE 2008 Paper 2 Offline
+4
-1

Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Column I Column II
(A) Potential energy of a simple pendulum (y-axis) as a function of displacement (x) axis (P)
(B) Displacement (y-axis) as a function of time (x-axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x-direction (Q)
(C) Range of a projectile (y-axis) as a function of its velocity (x-axis) when projected at a fixed angle (R)
(D) The square of the time period (y-axis) of a simple pendulum as a function of its length (x-axis) (S)

A
A$$\to$$(P, S); B$$\to$$(Q, S); C$$\to$$(S); (D)$$\to$$(Q)
B
A$$\to$$(S); B$$\to$$(Q, S); C$$\to$$(S); (D)$$\to$$(Q, S)
C
A$$\to$$(P, S); B$$\to$$(Q); C$$\to$$(S); (D)$$\to$$(Q, S)
D
A$$\to$$(S); B$$\to$$(Q, S); C$$\to$$(S, P); (D)$$\to$$(Q)
4
IIT-JEE 2008 Paper 2 Offline
+4
-1

An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Column I Column II
(A) (P) Real Image
(B) (Q) Virtual Image
(C) (R) Magnified Image
(D) (S) Image at infinity

A
A$$\to$$(P, Q, R); B$$\to$$(Q); C$$\to$$(P, R, S); D$$\to$$(P, Q, R, S)
B
A$$\to$$(P, Q, R, S); B$$\to$$(Q); C$$\to$$(P, Q, R, S); D$$\to$$(P, Q, R, S)
C
A$$\to$$(P, Q, R); B$$\to$$(Q); C$$\to$$(P, R, S); D$$\to$$(P, Q, S)
D
A$$\to$$(P, Q); B$$\to$$(Q); C$$\to$$(R, S); D$$\to$$(P, Q, R, S)
EXAM MAP
Medical
NEET