Please be patient as the PDF generation may take up to a minute.

1.

A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the path followed by its center of mass?

1.		2.
3.		4.

2. Consider two uniform discs of the same thickness and different radii \(R_1=R\) and \(R_2=\alpha R\) made of the same material. If the ratio of their moments of inertia, \(I_1\) and \(I_2,\) respectively, about their axes is \(I_1:I_2=1:16,\) then the value of \(\alpha\) is:
1. \(\sqrt{2}\)
2. \(4\)
3. \(2\)
4. \(2\sqrt{2}\)

3.

A bob of mass m attached to an inextensible string of length l is suspended from vertical support.  The bob rotates in a horizontal circle with an angular speed $\mathrm{\omega }$ $\mathrm{rad}/\mathrm{s}$ about the vertical.  About the point of suspension.

1.	Angular momentum is conserved
2.	Angular momentum changes in magnitude but not in the direction
3.	Angular momentum changes in direction but not in magnitude
4.	Angular momentum changes both in direction and magnitude

4.

A uniform cubical block of side L rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force F is applied on the block as shown. If there is sufficient friction between the block and the ground, then the torque due to normal reaction about its centre of mass is:

1.  $Zero$
2.  $FL$
3.  $\frac{FL}{2}$
4.  $\frac{3FL}{2}$

5.

A disc of radius \(2~\text{m}\) and mass \(100~\text{kg}\) rolls on a horizontal floor. Its centre of mass has a speed of \(20~\text{cm/s}\). How much work is needed to stop it?

1.	\(1~\text{J}\)	2.	\(3~\text{J}\)
3.	\(30~\text{J}\)	4.	\(2~\text{J}\)