Study questions platform-wide or filter by specific tests with correct answers revealed.
Total distance covered in 25 s \(= 20 \times 25 = 500\) m
Length of bridge \(= 500 - 100 = 400\) m
The dimensional formula of angular momentum is:
Angular momentum $L = I\omega = mvr$ (for a particle)
$[L] = [m][v][r] = M \cdot LT^{-1} \cdot L = ML^2T^{-1}$
This is the same as the dimension of Planck's constant $h$, which makes sense since $E = h\nu$ and angular momentum appears in quantum mechanics through $\hbar = h/2\pi$.
For $x\in\mathbb{R}$, let $f(x)=|\log 2-\sin x|$ and $g(x)=f(f(x))$. Which of the following is correct?
Since $\log 2 \approx 0.693$ and $\sin 0=0$, we have $f(0)=\log 2 > 0$.
Near $x=0$: $f(x)=\log 2-\sin x$ (since $\log 2>\sin x$ locally). So $f$ is smooth near $x=0$.
$g(x) = f(f(x)) = |\log 2 - \sin(f(x))|$. At $x=0$: $f(0)=\log 2$, so $\sin(f(0))=\sin(\log 2)$. Since $\log 2 < 1 < \pi$, $\sin(\log 2)>0$.
$g(0) = \log 2 - \sin(\log 2) > 0$, so near $x=0$, $g(x)=\log 2 - \sin(f(x))$.
$g'(0)=-\cos(f(0))\cdot f'(0)=-\cos(\log 2)\cdot(-\cos 0)=\cos(\log 2)$
Sign in to join the conversation and share your thoughts.
Log In to Comment