Crack the Problem

There are two columns. Each option on the left column may have one or more than one match on the right column. Answer is accepted as fully correct if all matches are correct.

Akshay Kulkarni from Raipur/Kota has come close to the final answer. Akshay has qualified in IIT JEE 2008.

There are two columns. Each option on the left column may have one or more than one match on the right column. Answer is accepted as fully correct if all matches are correct.

Many got few matches correct but no reply could be considered as fully correct or very close.

There are two columns. Each option on the left column may have one or more than one match on the right column. Answer is accepted as correct only if all matches are correct.

Consider a voltaic cell. Your decision to choose a match should not be based on, "may be" but should be based on, "must be".

Aashwin Gaur from Gwalior has come very close to the final answer.

There are two columns. Each option on the left column may have one or more than one match on the right column. Answer is accepted as correct only if all matches are correct.

R is the radius of the shell/sphere. r is the variable distance from the centre. Assume uniform charge distribution.

Cracked By:

Ajitabh Gupta, Jhansi
Shuchi Ojha, Delhi

There are two columns. Each option on the left column may have one or more than one match on the right column. Answer is accepted as correct only if all matches are correct.

Cracked By:

Sinjan Jana, 12th, Bishop Cotton Boys School, Bangalore.

There are two columns. Each option on the left column may have one or more than one match on the right column. Answer is accepted as correct only if all matches are correct.

Cracked By:

Lokesh Sardana, 12th Pass, D.A.V. School, Fatehabad, Haryana. Lokesh has qualified in IIT JEE 2008.

Chain of bicycle moves through two sprockets, a big and a small, the bigger one is towards the paddle side and the smaller one is towards the rear wheel side (refer figure).

Consider a bicycle in which the bigger sprocket has:
Teeth: N₁, Radius: r₁, Angular speed: \(\omega_1\)

And the smaller sprocket has:
Teeth: N₂, Radius: r₂, Angular speed: \(\omega_2\)

Let the linear speed of chain be v.

Find a relationship between \(\omega_1\) and \(\omega_2\).



Cracked By:

• Subhrashis Guha Niyogi, Class 12, B. E. College Model School, Howrah (provided full answer with solution). Subhrashis has qualified in IIT JEE 2008.
• Lokesh Sardana, 12th Pass, D.A.V. School, Fatehabad, Haryana (provided relation of \(\omega\) with r)
  
• Kartik M Mankad, 11th, Delhi Public School, Vadodara (provided relation of \(\omega\) with r).

Solution

Solution provided by Subhrashis Guha Niyogi (edited version):

Since chain is moving with constant linear speed,

\(\omega_1 \times r_1= \omega_2 \times r_2\)

So, \(2\pi r_1 \times w_1= 2\pi r_2 \times w_2\)

So, \(circumference \times \omega = constant\)

For chain to fit properly on both sprockets, teeth must be equally spaced.

So, \(circumference\alpha N\)

So, \(N\times \omega = constant\)

Hence, \(N_1\omega_1=N_2\omega_2\)

Find all numbers \(\alpha\) for which \(
\int\limits_1^2 {\left[ {\alpha ^2 + (4 - 4\alpha )x + 4x^3 } \right]dx \le 12}
\).

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Submission Closed, Answer: 3

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Cracked By:

• Anit Kumar Sahu, 12th, Ispat English Medium School, Sector-20, Rourkela. Anit has qualified in IIT JEE 2008.
  
• Ankul Garg, 12th Pass, Bal Bharati Public School, Rohini, Delhi. Ankul has qualified in IIT JEE 2007.
• Lokesh Sardana, 12th Pass, D.A.V. School, Fatehabad, Haryana.
  

Acetyl salicylic acid i.e. aspirin ionises in water as:

\(HC_9H_7O_4+H_2O \rightleftharpoons H_3O^+ + C_9H_7O^-\); K_a=2.75 x 10^-9.

What is the pH of the solution obtained by dissolving two tablets of aspirin in 250 mL of water? Assume that each tablet contains 0.32 gm of acetyl salicyclic acid.

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Submission Closed

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Cracked By:

Anit Kumar Sahu, 12th, Ispat English Medium School, Sector-20, Rourkela

Answer: 5.2

Match the following (more than one and non-unique matches are possible). Answer will be considered as correct only if all matches are correct:

(a) Kinetic energy of the system is conserved	(p) Elastic collision
(b) Kinetic energy of the system is not conserved	(q) Inelastic collision
(c) Linear momentum of the system is conserved	(r) No net external force
(d) Position of centre of mass remains unchanged	(s) Isolated two large bodies system in space in which both bodies are initially at rest
	(t) Uniform circular motion

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Submission Closed

Answer/Solution:

(a)-(p),(t)

Kinetic energy of a system is conserved in elastic collision. When there is no net external force, the kinetic energy need not be conserved as internal forces can do work and change kinetic energy. It is constant in uniform circular motion but in the case of isolated system of large bodies, since the bodies are large we must consider gravitational force between them which can change kinetic energy.

(b)-(q),(s)

In inelastic collision, kinetic energy of the system is not conserved. In case of isolated system of large bodies, the kinetic energy will change due to the gravitational force which is an internal force.

(c)-(p),(q),(r),(s)

Linear momentum is conserved whenever there is no net external force, irrespective of the type of collision.

(d)-(s)

Note that the option says "position" of centre of mass. When bodies are moving in elastic or inelastic colission centre of mass is moving and hence its position if not fixed. When there is no net external force, even then centre of mass can move with constant velocity and hence its position does not have to be fixed. In uniform circular motion, centre of mass does not necessary have a fixed positon.