to\[t=6\,s\]of the journey is: [BHU M-2003]
A) 1: 4: 9
B) 1: 2: 4
C) 1: 3: 5
D) 1: 2: 3
Correct Answer: C
Solution :
Key Idea: Since body is falling from rest initial velocity is zero. From the equation of motion, we have \[s=ut+\frac{1}{2}g{{t}^{2}}\] Where \[u\] us initial velocity\[\left( =\,0 \right)\], g is acceleration due to gravity and \[t\] is time. Let distance travelled in\[2s\], 4s and 6s be\[{{s}_{2}},\,{{s}_{4}},\,{{s}_{6}}\] then \[{{s}_{2}}=\frac{1}{2}g{{\left( 2 \right)}^{2}}=2g\] \[{{s}_{4}}=\frac{1}{2}g{{\left( 4 \right)}^{2}}=8g\] \[{{s}_{6}}=\frac{1}{2}g{{\left( 6 \right)}^{2}}=18g\] Distance travelled in first two seconds is \[{{\left( {{s}_{i}} \right)}_{2}}={{s}_{2}}-{{s}_{0}}=2g\] Similarly \[\left( {{s}_{{{m}_{2}}}} \right)={{s}_{4}}-{{s}_{2}}=8g-2g=6g\] \[\left( {{s}_{{{m}_{3}}}} \right)={{s}_{6}}-{{s}_{4}}=18g-8g=10g\] Hence, ratio is \[2g:6g:10g=1:3:5\]
You need to login to perform this action.
You will be redirected in
3 sec
