Answer

Verified

51.9k+ views

**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,

$mg\sin \theta \times s = \dfrac{1}{2}k{x^2}$

Where, $m$ is the mass of the block, $g$ is the acceleration due to gravity, $\theta $ 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, $m = \sqrt 2 \,kg$,

The spring constant is given as, $k = 100\,N{m^{ - 1}}$,

The compression of the spring is given as, $x = 1\,m$.

Now,

The work done by the block will be equal to the potential energy stored by the spring is given by,

$\Rightarrow$ $mg\sin \theta \times s = \dfrac{1}{2}k{x^2}\,...................\left( 1 \right)$

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,

$\Rightarrow$ $\sqrt 2 \times 10 \times \sin {45^ \circ } \times s = \dfrac{1}{2} \times 100 \times {1^2}$

From the trigonometry, the value of the $\sin {45^ \circ } = \dfrac{1}{{\sqrt 2 }}$, then the above equation is written as,

$\sqrt 2 \times 10 \times \dfrac{1}{{\sqrt 2 }} \times s = \dfrac{1}{2} \times 100 \times {1^2}$

By cancelling the same terms in the above equation, then the above equation is written as,

$\Rightarrow$ $10 \times s = \dfrac{1}{2} \times 100 \times {1^2}$

By rearranging the terms in the above equation, then the above equation is written as,

$\Rightarrow$ $s = \dfrac{{1 \times 100 \times {1^2}}}{{2 \times 10}}$

By multiplying the terms in the above equation, then the above equation is written as,

$s = \dfrac{{100}}{{20}}$

By dividing the terms in the above equation, then the above equation is written as,

$\Rightarrow$ $s = 5\,m$

**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.

Recently Updated Pages

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Which of the following amino acids is an essential class 12 chemistry JEE_Main

Which of the following is least basic A B C D class 12 chemistry JEE_Main

Out of the following hybrid orbitals the one which class 12 chemistry JEE_Main

Other Pages

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

According to classical free electron theory A There class 11 physics JEE_Main

In Bohrs model of the hydrogen atom the radius of the class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

In projectile motion the modulus of rate of change class 11 physics JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main