Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

A block of mass 2kg is released from the top of an inclined and smooth surface as shown in figure. If thee spring constant of spring is 100Nm1 and block comes to rest after compressing the spring by 1m, then the distance travelled by the block before it comes to rest is:

(A) 1m
(B) 1.25m
(C) 2.5m
(D) 5m

Answer
VerifiedVerified
153.9k+ views
like imagedislike image
Hint The distance travelled by the block before it comes to rest can be determined by using the statement that the work done by the block will be equal to the potential energy stored by the spring, by equating the two formulas, then the distance is determined.
Useful formula:
The work done by the block will be equal to the potential energy stored by the spring is given by,
mgsinθ×s=12kx2
Where, m is the mass of the block, g is the acceleration due to gravity, θ is the angle of the inclination, s is the distance travelled by the block, k is the spring constant and x is the compression of the spring.

Complete step by step answer
Given that,
The mass of the block is given as, m=2kg,
The spring constant is given as, k=100Nm1,
The compression of the spring is given as, x=1m.
Now,
The work done by the block will be equal to the potential energy stored by the spring is given by,
mgsinθ×s=12kx2...................(1)
By substituting the mass of the block, acceleration due to gravity, the angle of the inclination, spring constant and the compression of the spring in the above equation (1), then the above equation (1) is written as,
2×10×sin45×s=12×100×12
From the trigonometry, the value of the sin45=12, then the above equation is written as,
2×10×12×s=12×100×12
By cancelling the same terms in the above equation, then the above equation is written as,
10×s=12×100×12
By rearranging the terms in the above equation, then the above equation is written as,
s=1×100×122×10
By multiplying the terms in the above equation, then the above equation is written as,
s=10020
By dividing the terms in the above equation, then the above equation is written as,
s=5m

Hence, the option (D) is the correct answer.

Note Energy can neither be created nor destroyed. The energy can be transferred from one form of the energy to the other form of the energy. Here, the potential energy of the block is converted to the spring energy, because the block from the definite height will have the potential energy and then the block compresses the spring.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
EMI starts from ₹3,487.34 per month
Select and buy