2021 RI Yr CT Sect B Soln

Raffles Institution Year 5-6 Physics Department 1 2021 Year 5 H2 Physics Term 3 Common Test Solution Section B 1 (a) 2 2 12 base unit of forcebase unit of pressure base unit of area kg m s m kg m s (shown) − −− = = = (b) ( )( ) ( ) ( ) 13 12 1 2 22 1 1 1 2 2 2 2 21 1 1 m kg m s kg molbase unit of m kg m s K mol K skg m s m kg m s s m kg s Z −− − −− − − −− − =   =   = = (c) (i) ( ) ( ) 12 12 12 4 2.5 100 2.5 800101100 20003 2 10 Pa (1 s.f.) pp pp pp ∆− =− ∆− = × = = × (ii) ( ) ( ) ( ) 6 12 0.80 0.02 10 Pa 0.80 0.02 MPa pp−= ± × = ± (d) (i) Systematic errors result in all the measurements being either above or below the true value by a fixed amount. Random errors result in the measurements being scattered about a mean value. These measurements have equal probability of being above or below the mean value. (ii) ( ) ( ) 12 12 113 22 0.03 2.5 0.001 1 1.7 1 2.8 13 si nce 3.34 100 0.153 2 100 2 100 2 0.08098 8.1% (2 s.f.) ppZr Lm T Z r pp L m T rdrd rd ∆−∆∆ ∆∆ ∆    = + ++ +    −     ∆∆   = + + + + = ⇒=       = = Comments (a) Students should not use square brackets [ ] as they represent dimensions and not units. Students must write “units of” of a physical quantity.

Raffles Institution Year 5-6 Physics Department 2 (b) The most common mistake is missing the power of ½ for the term in square root. Students who are weak in manipulating algebraic expressions tend to get this wrong. (c) (i) The pressure gauge measures the pressure difference directly, and the percentage uncertainty of 2.5% refers to the pressure difference. Weaker students erroneously double the percentage uncertainty to 5%. (ii) Those who got this wrong tend to miss out the “mega” prefix in “MPa”, or they presented inconsistent decimal places for the numerical values. (d) (i) Many were careless in their use of terminologies in their statements. Marks were not awarded for inaccurate descriptions. (ii) Common mistakes include: using r = d/2, but not ∆r = ∆d/2; missing out factor of 3 for percentage error in r; missing out factor of ½ for percentage error in m and T; not using the given 2.5% for percentage error in ∆(p1 − p2). 2 (a) (i) Take direction upwards and to the right as positive. Consider the trajectory of the arrow from the archer to the cauldron. Vertically: ( )( ) 22 2 1 2 0 2 9.81 24 470.88 21.70 m s yyyy y y v u as u u − = + = +− = = ( )0 21.70 9.81 2.21 2.2 s (shown) yyyv u at t t = + = +− = = (ii) Since there is no air resistance, horizontal component of the velocity of the arrow remains constant throughout and acceleration in the horizontal direction is zero. 1 60 2.2 27.27 27.3 m s xx x x s ut su t − = = = = = (iii) 1 tan 21.70tan 27.27 38.51 38.5 y x u uθ θ − = =  = = °

Raffles Institution Year 5-6 Physics Department 3 (b) (i) (ii) cart’s