(SAJC) 2024 H2 Phy Prelim P3 soln_for sharing

1 SAJC 2024 Prelims / 9749 [Turn Over JC2 Prelim (H2 Physics) Paper 3 Solutions 1 (a)(i) Period of Earth, T = 24 x 3600 s (= 86 400 s) Angular velocity = 2π/T = 7.27 x 10-5 rad s-1 (shown) [1] (a)(ii) a = r2 = ( 6.38 x 106 ) x [Ans in (b) (i)]2 = 0.0337 m s-2 [1] [1- ecf] (b)(i) ● There is circular motion at the equator but not at the poles, ● At the equator, part of the gravitational force is used to provide the centripetal force (required to keep any mass located there in circular motion, centripetal force is provided by the gravitational force of Earth) (Hence only the remaining part of the gravitational force is available to provide the acceleration of free fall. ) Or ● Gravi force of Earth = (mg + mac)equa = (mg + mac)pole. [1] ● Since ac at pole = 0, gpole > gequa , ie g is different for the 2 locations[1] Note: g = acceleration of free fall as defined by the question not gravitational field strength. Be careful in use of symbols. [1] [1] (b)(ii) ● Value of g, at the pole is 9.81 m s-2 ● Since centripetal acceleration at equator (in b(ii)) is 0.0337 m s-2 , compared to 9.81 m s-2, the difference in g at these 2 locations is small. [1] [1] (c)(i) The gravitational force of attraction between two point masses is proportional to the product of their masses and inversely proportional to the square of their separation. [1] (c) (ii) (By Newton’s law), Gravitational force on a (point) mass m at Earth’s surface, F = 𝐺𝑀𝑚 𝑅2 Since field strength g is the gravitational force per unit mass at that point, g = F/m = 𝐺𝑀 𝑅2 [1] [1] (d)(i) ● { Since the gravitational force provides the centripetal force, } 𝐺𝑀𝑚 𝑟2 = mr2 {where r = dist of satellite fr Earth’s centre} [1]

2 SAJC 2024 Prelims / 9749 [Turn Over ( r3 = GM/2 , not assessed) -- (1) ● From (c), GM = gR2 -- (2) { R = Earth’s radius } (2) into (1): (r3 = gR2/2 , not assessed) ● Substituting, r = 4.23 x107 m {g = 9.81 m s-2, R= 6.38 x 106 m, = 7.27 x 10-5 rad s-1} [1] [1] (d)(ii) 1. Satellite lies on the equatorial plane of the earth 2. Satellite rotates/revolves from west to east or, following the Earth’s rotation [1] [1] 2(a) Volume decreases ; hence w is positive (or small volume change so w is 0) As the ice changes state, heat must have been supplied; hence q is positive. internal energy increases [1] [1] [1] (b) gas expands/increase