Units and Algebra: Maths Diagnostic

Descripción

If you can not do all of these problems, practice the resources at www.mathscentre.ac.uk
Jackie Grant
Creado por Jackie Grant
Jackie Grant
Creado por Jackie Grant hace más de 10 años
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Resumen del Recurso

Pregunta 1

Pregunta
\(\rm {The \ length \ of \ one \ side \ of \ a \ cube \ is \ 5.00 \ cm. \\ What \ is \ the \ volume \ in \ m^3 \ ?} \)
Respuesta
  • \( 1.25 \times 10^2 \ \rm m ^3\)
  • \( 1.25 \times 10^{-2} \ \rm m ^3\)
  • \( 1.25 \times 10^{-4} \ \rm m ^3\)
  • \( 1.25 \times 10^{-6} \ \rm m ^3\)
  • \( 1.25 \times 10^{-8} \ \rm m ^3\)

Pregunta 2

Pregunta
\(\rm {The \ density \ of \ aluminium \ is \ 2.70 \ g cm^{−3}, \\ convert \ this \ density \ to \ kg m^{−3}}. \)
Respuesta
  • \( 2.70 \times 10^{-9} \ \rm kgm ^{-3}\)
  • \( 2.70 \times 10^{-6} \ \rm kgm ^{-3}\)
  • \( 2.70 \times 10^{-1} \ \rm kgm ^{-3}\)
  • \( 2.70 \times 10^{3} \ \rm kgm ^{-3}\)
  • \( 2.70 \times 10^{6} \ \rm kgm ^{-3}\)

Pregunta 3

Pregunta
\( \rm{Calculate \ {\it a} \ in \ ms^{-2}, \ where \ {\it V} = 72 \ km/h \ and \ {\it R} = 2000 \ m, \\ from \ the \ equation \ {\it a} =\frac{ V^2}{R} } \)
Respuesta
  • \(2.0 \times 10^{1} { \rm \ ms^{-2}} \)
  • \(7.2 \times 10^{2} { \rm \ ms^{-2}} \)
  • \(2.6 \times 10^{0} { \rm \ ms^{-2}} \)
  • \(2.0 \times 10^{-1} { \rm \ ms^{-2}} \)
  • \(7.2 \times 10^{3} { \rm \ ms^{-2}} \)

Pregunta 4

Pregunta
\( {\rm Given} \ \pi r^2v = 5.2 \times 10^{-6} \ \rm {m^3 s^{-1}}, \\ find \ the \ value \ of \ { \it v} \ if \ {\it r} = 3.6 \ mm. \)
Respuesta
  • \(1.3 \times 10^{-1} \rm \ m s^{-1} \)
  • \(1.3 \times 10^{-7} \rm \ m s^{-1} \)
  • \(2.3 \times 10^{-4} \rm \ m s^{-1} \)
  • \(4.6 \times 10^{-4} \rm \ m s^{-1} \)
  • \(4.6 \times 10^{-7} \rm \ m s^{-1} \)

Pregunta 5

Pregunta
\( \rm The \ mass \ of \ a \ proton \ can \ be \ expressed \ as \ 1.0 {\it \ u}, \ where \ {\it u} \ is \ the \ Atomic \ Mass \ Unit \ and \ 1 \ {\it u} = 1.67\times 10^{−27} kg. \\ If \ a \ proton \ has \ a \ mass \ 2,000 \ times \ the \ mass \ of \ an \ electron, \ determine \ the \ energy, \ {\it E}, \ of \ an \ electron \ from \ its \ mass, \ {\it m}, \\ and \ the \ speed \ of \ light \ {\it c} = 3.0 \times 10^8 m s^{−1}, \ using \ the \ relationship \ between \ energy \ and \ mass \ given \ by \ \it E = mc^2. \)
Respuesta
  • \( 7.5 \times 10^{−14} \ \rm kg m^ 2 s^{−2} \)
  • \( 1.5 \times 10^{−10} \ \rm kg m^ 2 s^{−2} \)
  • \( 2.5 \times 10^{−22} \ \rm kg m^ 2 s^{−2} \)
  • \( 2.2 \times 10^{−14} \ \rm kg m^ 2 s^{−2} \)
  • \( 5.0 \times 10^{−19} \ \rm kg m^ 2 s^{−2} \)

Pregunta 6

Pregunta
\( P_2 = \rho g h + P_1 \ {\rm and} \ Q = \frac{\pi R^4(P_2−P_1)}{8\eta L}. \\ \rm Eliminate \ {\it P_1} \ and \ {\it P_2} \ and \ write \ an \ equation \ for \ {\it h} \ in \ terms \ of \ \it Q, \ R, \ ρ, \ g, \ \eta \ {\rm and} \ L. \)
Respuesta
  • \( h = \frac{8 \eta L Q}{\pi R^4 \rho g} \)
  • \( h = \frac{8 \eta L Q}{\pi R^4 } - \rho g \)
  • \( h = \frac{8 \eta L Q - \pi R^4}{\pi R^4 \rho g} \)
  • \( h = \frac{8 \eta L Q - \pi R^4}{\rho g} \)
  • \( h = \frac{ \pi R^4 - 8 \eta L Q -}{ \rho g} \)

Pregunta 7

Pregunta
\( \rm Determine \ the \ uncertainty \ in \ density, \sigma_{\rho}, \ in \ kg m^{−3}, \ of \ a \ cube \ of \ Manganese, \ if \ for \ a \ given \ set \ of \ measurements \\ length \ {\it l} = 3 \ cm, \ mass \ {\it m} = 2 \times 10^{-1} \ kg, \ uncertainty \ in \ length, \ \sigma_{\it l} = 5 \times 10^{-3} m, \ and \ uncertainty \ in \ mass, \ \sigma_{\it m} = 2 \ g, \\ using \ the \ equation \) \[ \sigma_\rho = \frac{\it m}{\it l^3}\sqrt{ \left(\frac{\sigma_{\it m}}{\it m}\right)^2 + 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2} \]
Respuesta
  • \( 2 \times 10^3 \rm \ kgm^{−3} \)
  • \( 5 \times 10^{-1} \rm \ kgm^{−3} \)
  • \( 2 \times 10^0 \rm \ kgm^{−3} \)
  • \( 5 \times 10^3 \rm \ kgm^{−3} \)
  • \(2 \times 10^{-1} \rm \ kgm^{−3} \)
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