Prove with the help of dimensional analysis that the equation $h = \frac{1}{2} g t$ for the distance travelled by a body falling freely under the gravity in time t is incorrect. Find the correct equation with the help of dimensions.

Open in App

Solution

Now if $R$ decrease
$\frac{m V_{n e w}^{2}}{r} = \frac{G M_{R} . m}{r_{n e w}^{2}}$
$V_{n e w} = \sqrt{\frac{G M_{E}}{r_{n e w}}}, V_{n e w} > V_{o l d}$
Hence, K.E increased.
Since, the work done is along the field. Hence the potential energy of system decreases.

Suggest Corrections

Similar questions

Q. The equation of motion of a body falling under gravity is given by

\frac{d v}{d t} = g - \frac{g}{λ^{2}} v^{2}

. Distance travelled as a function of time is given by?. Give at

v = 0

t = 0

Q. Assertion :The given equation

x = x_{0} + u_{0} t + \frac{1}{2} a t^{2}

is dimensionally correct, where x is the distance travelled by a particle in time t, initial position

x_{0}

, initial velocity

u_{0}

and uniform acceleration a is along the direction of motion Reason: Dimensional analysis can be used for checking the dimensional consistency or homogeneity of the equation.

Q. A body at rest is falling freely under gravity. The distance travelled by the body in the first 3 s is equal to the distance traveled by the same body in the same body in the nth second. What is the value of n?

Q. A body falls freely under gravity from rest and reaches the ground in time

t

. Write expression for the height fallen by the body.

Show that the sum of kinetic energy and potential energy(i.e., total mechanical energy) is always conserved in the case of freely falling body under gravity (with air resistance neglected) from a height h by finding it when (i) the body is at the top, (ii) the body has fallen a distance x, (iii) the body has reached the ground.

Join BYJU'S Learning Program

Prove with the help of dimensional analysis that the equation h=12gt for the distance travelled by a body falling freely under the gravity in time t is incorrect. Find the correct equation with the help of dimensions.

Now if R decreasemV2newr=GMR.mr2newVnew=√GMErnew,Vnew>VoldHence, K.E increased.Since, the work done is along the field. Hence the potential energy of system decreases.

Prove with the help of dimensional analysis that the equation $h = \frac{1}{2} g t$ for the distance travelled by a body falling freely under the gravity in time t is incorrect. Find the correct equation with the help of dimensions.

Now if $R$ decrease
$\frac{m V_{n e w}^{2}}{r} = \frac{G M_{R} . m}{r_{n e w}^{2}}$
$V_{n e w} = \sqrt{\frac{G M_{E}}{r_{n e w}}}, V_{n e w} > V_{o l d}$
Hence, K.E increased.
Since, the work done is along the field. Hence the potential energy of system decreases.