Answer

Verified

384k+ views

**Hint:**For the block to appear constant relative to the block, the force pulling the block must create an acceleration which would balance the acceleration due to the weight component of the body. The horizontal force on the block can be modelled according to Newton’s second law.

Formula used: In this solution we will be using the following formulae;

\[W = mg\] where \[W\] is the weight of a body, \[m\] is the mass, and \[g\] is acceleration due to gravity.

\[F = ma\] where \[F\] is the force acting on a body, and \[a\] is the net acceleration of the body.

**Complete Step-by-Step solution:**

For the block to appear constant relative to the block, the force pulling the block must create an acceleration which would balance the acceleration due to the weight component of the body.

Now, the weight component of the body is simply

\[{W_p} = W\sin \theta = mg\sin \theta \] since (\[W = mg\] where \[W\] is the weight of a body, \[m\] is the mass, and \[g\] is acceleration due to gravity).

Now, the acceleration of the entire wedge is shown to be horizontal. The force acting on the block due to this force causing the acceleration would be given from newton’s law (which is\[F = ma\] where \[F\] is the force acting on a body, and \[a\] is the net acceleration of the body) as

\[{F_b} = ma\]

Now, the component of the force in the same direction as the weight component is

\[{F_p} = ma\cos \theta \]

Since, they must be equal, we have

\[mg\sin \theta = ma\cos \theta \]

Hence,

\[a = g\dfrac{{\sin \theta }}{{\cos \theta }} = g\tan \theta \]

**The correct option is D**

**Note:**For clarity, the acceleration points in the same direction as the weight component because, if the wedge is moved forward, due to inertia, the block is though it’ll move backward. This backward fictitious force is equal to the real forward force acting on the wedge.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE