A small solid sphere rolls without slipping from rest at A, leaves the track horizontally at B and strikes the ground at C. For a=1.5 m and b=1.2 m, which option correctly gives both (i) the speed at C and (ii) the horizontal distance c?

Question

G1 Physics · Accepted Answer

For the rolling sphere, mechanical energy is conserved on the track: mgh+½mv²+½(2mr²/5)(v²/r²)=constant. This gives the speed at B. After leaving horizontally, the vertical impact component follows (vertical speed)²=2gb and the horizontal distance is c=vᵦ√(2b/g). Substituting a=1.5 m and b=1.2 m gives impact speed 6.68 m/s and horizontal distance 2.27 m. Hence option D.