Class 11th

Class 11th System of Particles and Rotational Motion

Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

Consider a fig in which m is mass of sphere and R is the radius having h height above the floor

The sphere will roll without slipping when w=v/r where v is linear velocity and w is angular velocity .

By conservation of momentum

mv (h-R)=Iw=2/5mR² (v/R)

mv (h-R)=2/5mvR

h-R=2/5R

so h = 7/5R .d $\to i$ sphere will roll here so no loss of energy.

Torque = F (h-R)

For torque=0 h=R sphere will have only translational motion. It would lose energy by friction.

b $\to i v$

the sphere will spin clockwise when t>0 so h>R

so c $\to i i$ and a $\to i i i$

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A uniform cube of mass m and side a is placed on a frictionless horizontal surface. A vertical force F is applied to the edge as shown in Fig. Match the following (most appropriate choice):

(a) mg/4 < F mg < /2 (i) Cube will move up.

(b) F > mg/2 (ii) Cube will not exhibit motion.

(c) F > mg (iii) Cube will begin to rotate and slip at A.

(d) F = mg/4 (iv) Normal reaction effectively at a/3 from A, no motion.

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Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

Moment of force $τ$ ₁= F (a)….anticlockwise

Moment of weight mg $τ$ ₂=mg (a/2)……. (clockwise)

Cube will not exhibit motion then $τ$ _{1
$= τ$}₂

$F * a = m g * \frac{a}{2}$

F=mg/2

Cube will rotate when $τ$ _{1
$> τ$}₂

$F * a > m g * \frac{a}{2}$

F>mg/2

At a/3 from point A then

mg $* \frac{a}{3} = F * a o r F = \frac{m g}{3}$

when F=mg/4 which is less then mg/3 there will be no motion.

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Aluminium dissolves in mineral acids and aqueous alkalies and thus shows amphoteric character. A piece of aluminium foil is treated with dilute hydrochloric acid or dilute sodium hydroxide solution in a test tube and on bringing a burning matchstick near the mouth of the test tube, a pop sound indicates the evolution of hydrogen gas. The same activity when performed with concentrated nitric acid, reaction does not proceed. Explain the reason.

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Class 11th Systems of Particles and Rotational Motion

Contributor-Level 10

This is a Short Answers Type Questions as classified in NCERT Exemplar

The following reaction takes place in the test tube

i) When Aluminium is treated with dilute hydrochloric acid.

Al + HCl -à AlCl₃

ii) When Aluminium is treated with dilute sodium hydroxide solution.

Al + NaOH -àNaAlO₂ + H₂

In both the cases, the Hydrogen atoms are evolved. So, when a burning match stick is brought near the test tube we hear a pop sound.

Aluminium does not react with concentrated nitric acid. A "layer" of "Aluminium Oxide" is formed, when aluminium reacts with the nitric acid because "nitric acid" is an oxidising agent. Due t

...more

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The variation of angular position θ , of a point on a rotating rigid body, with time t is shown in Fig. Is the body rotating clock-wise or anti-clockwise?

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Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

As the slope of graph is positive and positive slope indicates anti clockwise rotation which is traditionally taken as positive.

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When BCl₃ is treated with water, it hydrolyses and forms [B(OH)₄]⁻only whereas AlCl₃ in acidified aqueous solution forms [Al(H₂0)₆]³⁺

Explain what is the hybridisation of boron and aluminium in these species?

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Class 11th System of Particles and Rotational Motion

Contributor-Level 10

This is a Short Answers Type Questions as classified in NCERT Exemplar

BCl₃+3H₂O→B (OH)₃+3HCl

B (OH)₃+2H₂O→ [B (OH)₄]⁻+H₃O⁺

B (OH)₃due to its incomplete octet accepts an electron pair (OH)^- to give has configucation [B (OH)₄]⁻.

Boron in this ion involves one 2s orbital and three 2p orbitals. Thus, hybridization of B in [B (OH)₄]⁻ is sp³

AlCl₃ + 6H₂O [Al (H₂O)₆]³⁺ +3Cl^-

Hence, hybridization of Al is sp³d²

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Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

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Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

The moment of inertia of the object I = $\sum m$ r² [sum of moment of inertia of each constituents particles]

All the mass in a cylinder lies at a distance R from the axis of symmetry but most of the mass of a solid sphere lies at a smaller distance than R.

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If a trivalent atom replaces a few silicon atoms in three dimensional network of silicon dioxide, what would be the type of charge on overall structure?

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Class 11th Systems of Particles and Rotational Motion

Contributor-Level 10

This is a Short Answers Type Questions as classified in NCERT Exemplar

When a trivalent atom is added to the crystal of SiO₂, it substitutes silicon atoms which result in generation of holes. These holes make the crystal conductor of electricity. The overall Crystal is electrically neutral and is called the p-type conductor.

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The centre of gravity of a body on the earth coincides with its centre of mass for a 'small' object whereas for an 'extended' object it may not. What is the qualitative meaning of 'small' and 'extended' in this regard ? For which of the following the two coincides? A building, a pond, a lake, a mountain?

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Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

When the vertical height of the objects is very small as compared to the earth's radius we call the objects small, otherwise it is extended. Building and ponds are small objects and deep lake and ocean are examples of extended objects.

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Carbon and silicon both belong to the group 14, but in spite of the stoichiometric similarity, the dioxides (i.e., carbon dioxide and silicon dioxide) differ in their structures. Comment.

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