In a new unit system, units of energy, momentum and force are 10, 5 and 2 times their SI units, respectively. The source states the new acceleration unit is n² times the SI acceleration unit. Find n.
Physics · Mixed Chapter
JEE Main Practice

Question

In a new unit system, units of energy, momentum and force are 10, 5 and 2 times their SI units, respectively. The source states the new acceleration unit is n² times the SI acceleration unit. Find n.

G1 Physics · Accepted Answer

Step 1: Since E/p has dimensions of velocity, new velocity unit = (10/5) = 2 SI velocity units. Step 2: Since E/F has dimensions of length, new length unit = 10/2 = 5 SI length units. Step 3: New time unit = 5/2 SI time units; new acceleration unit = 5/(5/2)² = 4/5 SI acceleration units. Step 4: Consequently n² = 4/5, not 25. The source key n = 5 conflicts with the stated unit factors.