What is the value of linear velocity if $\overrightarrow r = 3\widehat i + 4\widehat j + 6\widehat k$ and $\overrightarrow \omega = -5\widehat i + 3\widehat j + 5\widehat k$ ?
What is the value of linear velocity if $\overrightarrow r = 3\widehat i + 4\widehat j + 6\widehat k$ and $\overrightarrow \omega = -5\widehat i + 3\widehat j + 5\widehat k$ ?
- A
$ - 2\widehat i + 45\widehat j - 29\widehat k$
- B
$ 2\widehat i - 45\widehat j + 29\widehat k$
- C
$3\widehat i - 29\widehat j + 45\widehat k$
- D
$5\widehat i - 6\widehat j + 4\widehat k$
Similar Questions
A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. $He /$ she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path xyz of radius $R$ during which he/she reaches a maximum height $h$ (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ( $g$ is the acceleration due to gravity)
$(A)$ $v_0^2-2 g h=\frac{1}{2} g R$
$(B)$ $v_0^2-2 g h=\frac{\sqrt{3}}{2} g R$
$(C)$ the centripetal force required at points $x$ and $z$ is zero
$(D)$ the centripetal force required is maximum at points $x$ and $z$
A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. $He /$ she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path xyz of radius $R$ during which he/she reaches a maximum height $h$ (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ( $g$ is the acceleration due to gravity)
$(A)$ $v_0^2-2 g h=\frac{1}{2} g R$
$(B)$ $v_0^2-2 g h=\frac{\sqrt{3}}{2} g R$
$(C)$ the centripetal force required at points $x$ and $z$ is zero
$(D)$ the centripetal force required is maximum at points $x$ and $z$
- [IIT 2020]
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