+1 vote
199 views
in Physics – Class 11 by (74.2k points)
A ring, disc and solid sphere are left from the top of an incline which has sufficient friction for pure rolling. Which will reach the bottom first, if they all have the same mass ‘M’ & radius ‘R’?

(a) Ring

(b) Disc

(c) Solid sphere

(d) All will reach together

I have been asked this question in my homework.

Query is from Rolling Motion in division System of Particles and Rotational Motion of Physics – Class 11

1 Answer

+1 vote
by (720k points)
selected by
 
Best answer
Correct option is (c) Solid sphere

Explanation: The equation of motions will be: Mgsinθ – f = Ma, where f is the friction & a is acceleration. Also, fR = Ia/R. From this equation ‘f’ will be substituted in the first equation: Mgsinθ – Ia/R^2 = Ma.

∴ a = Mgsinθ / (I/R^2+ M). Thus, more the value of I lesser will be the acceleration.

Moment of inertia of ring = MR^2

Moment of inertia of disc= MR^2/2

Moment of inertia of solid sphere = 2MR^2/5

The solid sphere has the least moment of inertia, so it will have the maximum acceleration & hence it will take the least time. Note that if there was no friction their accelerations would be the same and they would reach together.

Related questions

Welcome to TalkJarvis QnA, a question-answer community website for the people by the people. On TalkJarvis QnA you can ask your doubts, curiosity, questions and whatever going in your mind either related to studies or others. Experts and people from different fields will answer.

Most popular tags

biology – class 12 biology – class 11 construction & building materials chemistry – class 12 electronic devices & circuits network theory data structures & algorithms ii cell biology ic engine insurance finance money computational fluid dynamics engineering physics i discrete mathematics chemistry – class 11 aerodynamics casting-forming-welding i engineering mathematics operating system casting-forming-welding ii engineering drawing mysql engineering geology digital circuits wireless mobile energy management electrical measurements digital communications cyber security analytical instrumentation embedded systems electric drives cytogenetics computer fundamentals life sciences basic civil engineering advanced machining iot design of electrical machines physics – class 12 applied chemistry dairy engineering basic chemical engineering cloud computing microprocessor bioinformatics aircraft design aircraft maintenance software engineering drug biotechnology digital signal processing biochemistry data structures & algorithms i automotive engine design avionics engineering material & metallurgy energy engineering cognitive radio unix electrical machines biomedical instrumentation object oriented programming electromagnetic theory power electronics analog communications bioprocess engineering civil engineering drawing engineering metrology physics – class 11 mathematics – class 12 engineering chemistry i basic electrical engineering unit processes mongodb signals and systems cryptograph & network security hadoop mathematics – class 11 engineering physics ii html control systems engineering mechanics antennas analog circuits computer network java sql server javascript concrete technology chemical process calculation artificial intelligence design of steel structures c++ database management computer architecture engineering chemistry ii corrosion engineering chemical technology dc machines
...