A force is represented by where = distance and = time. The dimensions of are

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A force is represented by $F = a x^{2} + b t^{1 / 2}$ where $x$ = distance and $t$ = time. The dimensions of $b^{2} / a$ are [2024]

1 $[M L^{2} T^{- 3}]$

2 $[M L^{3} T^{- 3}]$

3 $[M L^{- 1} T^{- 1}]$

4 $[M L T^{- 2}]$

Ans.
(2)

$F = a x^{2} + b t^{1 / 2}$

$[a] = \frac{[F]}{[x^{2}]} = [M^{1} L^{- 1} T^{- 2}]$

   $[b] = \frac{[F]}{[t^{1 / 2}]} = [M^{1} L^{1} T^{- 5 / 2}]$

   $[\frac{b^{2}}{a}] = \frac{[M^{2} L^{2} T^{- 5}]}{[M^{1} L^{- 1} T^{- 2}]} = [M^{1} L^{3} T^{- 3}]$

Want Us to Email you About Special Offers & Updates?