Answer

Verified

46.2k+ views

**Hint:**In order to solve the given question, first of all we need to find the value of $x$. After that we can put the value of $x$ in the equation for maximum height and get the required value. Now, for finding the value of $x$ we need to find the slope of the curve and we need to find the forces acting in the horizontal direction. Then we can finally conclude with the correct solution of the given question.

**Complete step by step solution:**

The shape of the parabolic bowl is given as, $y = \dfrac{{{x^2}}}{{20}}$

Now, let us find the slope of the bowl. So, the equation can be written as,

$\Rightarrow \tan \theta = \dfrac{{dy}}{{dx}}$

$ \Rightarrow \tan \theta = \dfrac{{d({x^2})}}{{dx(20)}} = \dfrac{{2x}}{{20}} = \dfrac{x}{{10}}$…………… (i)

We know that in the horizontal direction,

$\Rightarrow \mu N\cos \theta = N\sin \theta $

$ \Rightarrow \tan \theta = \mu $……………….. (ii)

The value of coefficient of friction is given as,$\mu = 0.5$

Now, from equation (i) and (ii), we can write it as,

$\Rightarrow \dfrac{x}{{10}} = 0.5$

$\therefore x = 5m$

Now, we need to find the maximum height. So, from the figure, for maximum height we need to take $y = \dfrac{{{x^2}}}{{20}}$.

After putting the value of $x$ in the above equation, we get,

$\Rightarrow y = \dfrac{{{x^2}}}{{20}} = \dfrac{{25}}{{20}} = \dfrac{5}{4} = 1.25m$

Therefore, the value of maximum height is $1.25m$.

**Hence, we can conclude that option (B), i.e. $1.25m$ is the correct choice of the given question.**

**Note:**From Newton’s third law of motion, we know that every action force has an equal reaction force which acts in the opposite direction. In case when the body is in a static position, the forces acting on the body have to be balanced or in other words we can say that their sum has to be zero.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main

Other Pages

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

Electric field due to uniformly charged sphere class 12 physics JEE_Main

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

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

How is a pn junction diode used as a half wave rectifier class 11 physics JEE_MAIN