10 Selected Qs - System of Particles & Rotation Motion - NCERT Examples & Back ExerciseContact Number: 852752171810 Selected Qs - System of Particles & Rotation Motion - NCERT Examples & Back ExerciseContact Number: 8527521718A metal bar \(70\) cm long and \(4.00\) kg in mass supported on two knife edges placed \(10\) cm from each end. A \(6.00\) kg load is suspended at \(30\) cm from one end as shown in the figure. The reactions \(R_1~\text{and}~R_2\) at the knife-edges are: (Assume the bar to be of uniform cross-section and homogeneous.)
1. \(43.12~\text{N}~\text{and}~54.88~\text{N}\)
2. \(54.88~\text{N}~\text{and}~4.312~\text{N}\)
3. \(54.88~\text{N}~\text{and}~43.12~\text{N}\)
4. \(43.12~\text{N}~\text{and}~5.488~\text{N}\)
A \(3~\text{m}\) long ladder weighing \(20~\text{kg}\) leans on a frictionless wall. Its feet rest on the floor \(1~\text{m}\) from the wall as shown in the figure. The reaction forces of the wall and the floor respectively are:
| 1. | \(30.4~\text{N}\) and \(198~\text{N}\) |
| 2. | \(199~\text{N}\) and \(30~\text{N}\) |
| 3. | \(30~\text{N}\) and \(199~\text{N}\) |
| 4. | \(34.6~\text{N}\) and \(199~\text{N}\) |
The moment of inertia of a disc about one of its diameters is:
| 1. | \(MR^2\) | 2. | \(\dfrac{MR^2}{3}\) |
| 3. | \(\dfrac{2MR^2}{3}\) | 4. | \(\dfrac{MR^2}{4}\) |
In the \(\mathrm{HCl}\) molecule, the separation between the nuclei of the two atoms is about \(1.27~\mathring{\text A}~(1~\mathring{\text A}=10^{10}~\text m).\) Then the approximate location of the CM of the molecule is:
(Given that a chlorine atom is about \(35.5\) times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus).
| 1. | \(1.235~\mathring{\text A}\) from \(\mathrm{H-}\)atom |
| 2. | \(2.41~\mathring{\text A}\) from \(\mathrm{Cl-}\)atom |
| 3. | \(3.40~\mathring{\text A}\) from \(\mathrm{Cl-}\)atom |
| 4. | \(1.07~\mathring{\text A}\) from \(\mathrm{H-}\)atom |
A non-uniform bar of weight \(W\) is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are \(36.9^\circ\) and \(53.1^\circ\) respectively. The bar is \(2\) m long. The distance \(d\) of the center of gravity of the bar from its left end is:
(Take sin\(36.9^\circ=0.6\) and sin\(53.1^\circ=0.8\))
1. \(69\) cm
2. \(72\) cm
3. \(79\) cm
4. \(65\) cm
A car weighs \(1800~\text{kg}.\) The distance between its front and back axles is \(1.8~\text m.\) Its center of gravity is \(1.05~\text m,\) behind the front axle. The force exerted by the level ground on each front wheel and each back wheel is respectively:
1. \(2680~\text N, ~5145~\text N\)
2. \(5145~\text N, ~3675~\text N\)
3. \(5145~\text N, ~5145~\text N\)
4. \(3675~\text N, ~5145~\text N\)
Given the moment of inertia of a disc of mass \(M\) and radius \(R\) about any of its diameters to be \(\dfrac{MR^{2}}{4},\) then the moment of inertia about an axis normal to the disc passing through a point on its edge is:
1. \(\dfrac{3}{2}MR^{2}\)
2. \(\dfrac{1}{4}MR^{2}\)
3. \(\dfrac{2}{5}MR^{2}\)
4. \(\dfrac{7}{5}MR^{2}\)
A rope of negligible mass is wound around a hollow cylinder of mass \(3\) kg and radius \(40\) cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of \(30\) N?
(Assume that there is no slipping.)
1. \(21\) rad/s2
2. \(24\) rad/s2
3. \(20\) rad/s2
4. \(25\) rad/s2
A meter stick is balanced on a knife edge at its center. When two coins, each of the mass \(5\) gm are put one on top of the other at the \(12.0\) cm mark, the stick is found to be balanced at \(45.0\) cm. What is the mass of the meter stick?
1. \(66~\text{gm}\)
2. \(56~\text{gm}\)
3. \(76~\text{gm}\)
4. \(79~\text{gm}\)
