Answer

Verified

448.8k+ views

**Hint:**In solving this question, first we will use the third equation of motion given by Newton and use it to find the value of the final velocity of the dumb-bell and then use the velocity we get in the calculation of the momentum of the body and that will be the momentum that will be transferred to the floor.

**Formula used:**$2as={{v}^{2}}-{{u}^{2}}$

**Complete step-by-step solution:**We will assume that when the dumb-bell falls to the floor, it does not bounce and remains on the floor i.e. all of its momentum gets transferred to the floor at the same moment. Now we will use the third equation of motion by Newton to find what will be the velocity of the dumb-bell just before it strikes the ground.

$2as={{v}^{2}}-{{u}^{2}}$

Here, a is the acceleration on the body (dumb-bell here) which here will be the acceleration due to gravity. Its magnitude has been given as 10 $m{{s}^{-2}}$ in the question.

s is the distance traveled by the body under that acceleration which here is given as 80 cm i.e. 0.8 m.

v is the final velocity of the dumb-bell and u will be its initial velocity.

We will take u to be zero as the body starts from rest and we will take the downward direction as positive. So,

\[\begin{align}

& 2\times 10\times 0.8={{v}^{2}}-{{0}^{2}} \\

& {{v}^{2}}=16 \\

& \therefore v=4m{{s}^{-1}} \\

\end{align}\]

The momentum of the body at that moment will be the product of its mass and velocity.

$P=mv=10\times 4=40kgm{{s}^{-1}}$

As all the momentum gets transferred, $40kgm{{s}^{-1}}$ will be transferred.

**Note:**The sign convention of the different quantities in the formula such as acceleration, displacement, and velocities used must be consistent with each other, positive for them must either be taken in the upwards direction or the downwards direction. We can also use the direct formula for the velocity of an object falling under gravity from rest which is $v=\sqrt{2gh}$.

Recently Updated Pages

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

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

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

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

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

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