A ball of mass m strikes a vertical wall with a speed v at an angle of θ to the wall. The ball rebounds at the same speed and angle. What is the change in the magnitude of the momentum of the ball?
A. 2 mv sin θ
B. 2 mv cos θ
C. 2 mv
D. zero
Answer/Explanation
Markscheme
B
Change in momentum in vertical downward direction is zero.
In horizontal direction taking right side positive
\(\Delta P = m ( Vcos\Theta – (- Vcos\Theta )\)
\(\Delta P= 2mvcos\Theta\)
A sealed cylinder of length l and cross-sectional area A contains N molecules of an ideal gas at kelvin temperature T.
What is the force acting on the area of the cylinder marked A due to the gas?
A. \(\frac{{NRT}}{l}\)
B. \(\frac{{NRT}}{{lA}}\)
C. \(\frac{{N{k_B}T}}{{lA}}\)
D. \(\frac{{N{k_B}T}}{l}\)
Answer/Explanation
Markscheme
D
\(PV=nRT\)
and, \(K_b=\frac{R}{N_a}\)
Volume of cylinder \(= A\times l\)
\(P=\frac{N_aK_bT}{A\times l}\)
And, \(Pressure = Force\times Area\)
putting the value of P .
\(F=\frac{N_aK_bT}{ l}\)
Which of the following is a value of wavelength that is found in the visible region of the electromagnetic spectrum?
A. \(4 \times {10^{ – 5}}{\text{ m}}\)
B. \(4 \times {10^{ – 7}}{\text{ m}}\)
C. \(4 \times {10^{ – 9}}{\text{ m}}\)
D. \(4 \times {10^{ – 11}}{\text{ m}}\)
Answer/Explanation
Markscheme
B
Question
A pipe of fixed length is closed at one end. What is \(\frac{{{\text{third harmonic frequency of pipe}}}}{{{\text{first harmonic frequency of pipe}}}}\)?
A. \(\frac{1}{5}\)
B. \(\frac{1}{3}\)
C. 3
D. 5
Answer/Explanation
Markscheme
C
For Pipe Closed at on end
\(L=(2n+1)\frac{\;\lambda}{4} \; where \; n=0,1,2,3 \; etc..\)
\(\because v=f\lambda\)
\(\therefore f=\frac{v}{\lambda}=\frac{2n+1}{4L}\times v\)
for first harmonic \(n =0\) and third harmonic (or first overtone)\( n=1\)
\(\frac{f_{n=1}}{f_{n=0}} =\frac{\frac{3}{4L}}{\frac{1}{4L}}=3\)