A pendulum clock loses 12 s a day if the temperature is 400C and gains 4 s a day if the temperature is 200C.  The temperature at which the clock will show correct time, and  the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively :

  • Option 1)

     250C;  α = 1.85×10−5/0C

     

  • Option 2)

     600C; α =1.85×10−4/0C

     

  • Option 3)

     300C; α=1.85×10−3/0C

     

  • Option 4)

     550C;  α = 1.85×10−2/0C

 

Answers (1)

As we learnt in

Time period of oscillation of simple pendulum -

T=2\pi \sqrt{\frac{l}{g}}

- wherein

l = length of pendulum 

g = acceleration due to gravity.

 

 Times lost / gained per day =\frac{1}{2}\times \alpha\times \Delta\theta\times 86,400\ sin\theta

Where \alpha-Co-efficient of linear expansion.

12=\frac{1}{2}\times(40-\theta)\times 86400                (i)

4=\frac{1}{2}\times(\theta-20)\times 86400                (ii)

On dividing we get

3=\frac{40-theta}{\theta-20}=3\theta-60=40\theta

\therefore\ \; 4\theta=100\ \; \Rightarrow\ \; \theta=25^{o}C

After put the value of \theta we get \alpha

\alpha=1.85\times 10^{-5}

Correct option is 1.


Option 1)

 250C;  α = 1.85×10−5/0C

 

This is the correct option.

Option 2)

 600C; α =1.85×10−4/0C

 

This is an incorrect option.

Option 3)

 300C; α=1.85×10−3/0C

 

This is an incorrect option.

Option 4)

 550C;  α = 1.85×10−2/0C

This is an incorrect option.

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions