A trolley of initial mass 18 kg moves with velocity v=3t m/s. Sand falls vertically into it at 18 kg/s and sticks. If dK/dt at t=2 s is 324n W, find n.
Physics · Mixed Chapter
JEE Main Practice

Question

A trolley of initial mass 18 kg moves with velocity v=3t m/s. Sand falls vertically into it at 18 kg/s and sticks. If dK/dt at t=2 s is 324n W, find n.

G1 Physics · Accepted Answer

Step 1: Mass of trolley plus collected sand M(t)=18+18t=18(1+t). Step 2: K=½Mv²=½×18(1+t)(3t)²=81t²(1+t). Step 3: Differentiate dK/dt=81(2t+3t²). Step 4: At t=2, dK/dt=81(4+12)=1296 W=324×4 W; n=4.