Let us consider an equaiton `(1)/(2)mv^2 = mgh,` Where m is the mass of the body, `upsilon` its velocity, g is acceleration due to gravity and h is the height. Cheak whether this equation is dimensionally correct.
Text Solution
Verified by Experts
The dimensions of LHS are `[M] [LT^(-1)]^(2)=[M] [L^(2)T^(-2)]` `= [M L^(2) T^(-2)]` the dimensions of RHS are `[M] [LT^(-2)] [L]=[M] [L^(2)T^(-2)]` `=[M L^(2) T^(-2)]` The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct.
Topper's Solved these Questions
UNITS AND MEASUREMENT
NCERT|Exercise EXERCISE|33 Videos
UNITS AND MEASUREMENT
NCERT|Exercise QUESTION|1 Videos
THERMODYNAMICS
NCERT|Exercise EXERCISE|10 Videos
WAVES
NCERT|Exercise EXERCISE|27 Videos
Similar Questions
Explore conceptually related problems
Let us consider an equation (1)/(2)muepsilon^2 = mgh, Where m is the mass of the body, upsilon its velocity, g is acceleration due to gravity and h is the height. Check whether this equation is dimensionally correct.
Find ratio of acceleration due to gravity g at depth d and at height h where d=2h
The velocity of a freely falling body changes as g^ph^q where g is acceleration due to gravity and h is the height. The values of p and q are
The displacement of a body is given by s=(1)/(2)g t^(2) where g is acceleration due to gravity. The velocity of the body at any time t is
The terminal velocity v of a small steel ball ofradius r fal ling under gravity through a column ofa viscous liquid of coefficient of viscosity eta depends on mass of the ball m, acceleration due to gravity g, coefficient of viscosity eta and radius r. Which of the following relations is dimensionally correct?
The Bernoulli's equation is given by P+1/2 rho v^(2)+h rho g=k . Where P= pressure, rho = density, v= speed, h=height of the liquid column, g= acceleration due to gravity and k is constant. The dimensional formula for k is same as that for:
A ball is thrown upwards . Its height varies with time as shown in figure. If the acceleration due to gravity is 7.5 m//s^(2) , then the height h is
An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by
Taking the value of the acceleration due toj gravity as 10 m s^(-2) , Find its value in km h^(-2).
Show dimensionally that the relation t = 2pi((I)/(g)) is incorrect, where I is length and t is time period of a simple pendulum , g is acc. Due to gravity. Find the correct form of the relation, dimensionally