Question

A solid brass sphere, an aluminum hoop, and a solid stainless steel cylinder are each allowed to roll down the entire length of a one-meter long plank that is inclined at an angle of 30 degrees to the horizontal. The density of brass is 8.50.1g/cmº), the density of aluminum is 2.60 [g/cm3), and the density of stainless steel is 7.50 [g/cm3]. A. Which object will reach the bottom of the plank in the shortest length of time? [5] (a) Can't tell. Need more information. (b) The sphere (c) The hoop (d) The cylinder 3. Which object has the largest moment of inertia? [5] (a) Can't tell. Need more information. (b) The sphere (c) The hoop (d) The cylinder Which object has the largest total kinetic energy when it reaches the bottom? [5] (a) Can't tell. Need more information. (b) The sphere c) The hoop d) The cylinder

Answer 1

sol" :- Given A solid brass sphere, p = 8.50 g/cm3 Aluminium hoop / sing. e -2.60 gems Solid Stainless steel ylinder the f = 7,5 g/cm3 Here, Radius for and size 18 not mentimed. Also, Given, palm, 0-1 Hoop selid cylinder solid sphere le lysing bettem 6 Applying the energy conservation at booka os Pixie KiE fotel - k-Efronet kiExot. mgh = I MV² + & JW 2 / 4 (Ww=4 / Lel. Mas of solid brass spheres My

i I sphere = 2 / / My R} (say radiuser and Walks Similarly, assuming hoopleing ? mau of hoopleing = me Aliminim and Radius = RH i I loob = Marx R Now, and, Mom of steunless steel tylinder = M so Radius= Rc I cylinder = b Mg R? From equation (t), nigh = $ 102 + 1 (ok) x 12 3 (1+kh) v2 = 2gh oo Tv= gght R² where, K = Radius of gyration For sphere, K=12 - RS For ring. Kring = kr

Jlindes- tz Receptes 50 and Kylinder- tag ke * Vagine alle spese) Neparere = 10x3.elx Holy Usphere 2.65 mis] 10x9.81% 1 ginilarly, Veing hoop / (1+1) 2x9.81 X 1 X Y Z and, and, L Hoop = 2.215 mls] Vylinder = 2x9.8x1x , Vaulinder (1+4) | Veylindo; = 2.557 mis Po length = m = omstant and in -> sphere > Veylinder > Hool "sphere will reach to the bottom with shortest length of time.

② As we know, moment of inertia of any object / badly I= mk² k= Radlies Herr [m= fx Volume 7 of gyreten, only density of boelies material is given whether there is no intormation about the dimension of body, so we would not be able to find out the moment of inertia of these bodies. Con't teet tell, Need more informath (C.) we have Total KiE = k. E trans. tk Exot, = b mua tho I A? = + mv² + mv2 / 2 AS m= fx Volume Anding volume, we need dimento of body, and it is not given, so can't tell need more infood se information