The force 7 i + 3 j - 5 k acts on a particle whose position vecto… - Vidyadip

MCQ

The force $7\widehat i + 3\widehat j - 5\widehat k$ acts on a particle whose position vector is $\widehat i - \widehat j + \widehat k$ . What is the torque of the given force about the origin ?

✓
$2 \widehat i +12\widehat j +10\widehat k$
B
$2\widehat i +10\widehat j +12\widehat k$
C
$2\widehat i +10\widehat j +10\widehat k$
D
$10\widehat i + 2\widehat j + \widehat k$

✓

Answer

Correct option: A.

$2 \widehat i +12\widehat j +10\widehat k$

a
Here, $\vec{r}=\hat{i}-\hat{j}+\hat{k}$

$\overrightarrow{\mathrm{F}}=7 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}$

Torque, $\vec{\tau}=\vec{r} \times \vec{F}$

$\vec{\tau}=\left|\begin{array}{rrr}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {1} & {-1} & {1} \\ {7} & {3} & {-5}\end{array}\right|=\hat{i}(5-3)+\hat{j}(7-(-5))+\hat{k}(3-(-7))$

or $\vec{\tau}=2 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}+10 \hat{\mathrm{k}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A cylindrical plastic bottle of negligible mass of filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega $. If the radius of the bottle is $2.5\, cm$ then $\omega $ is close to ..... $rad\, s^{-1}$ (density of water $= 10^3\, kg/m^3$)

For a convex lens the distance of the object is taken on $X$-axis and the distance of the image is taken on $Y$-axis, the nature of the graph so obtained is

A bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3,$ how far will the block slide approximately?

Two batteries with e.m.f $12\ V$ and $13\ V$ are connected in parallel across a load resistor of $10\,\Omega$ . The internal resistances of the two batteries are $1\,\Omega$ and $2\,\Omega$ respectively. The voltage across the load lies between

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10 \pm 0.1 \mathrm{~cm}$ and the distance of its real image from the lens is $20 \pm 0.2 \mathrm{~cm}$. The error in the determination of focal length of the lens is $n \%$. The value of $n$ is. . . . . . .

A finite ladder is constructed by connecting several sections of $2\,\mu F,\;4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between......$\mu F$

In a given series $LCR$ circuit $R = 4\, \Omega, X_L = 5\, \Omega$ and $X_C = 8\, \Omega$, the current :-

A block is attached to a spring as shown and very-very gradually lowered so that finally spring expands by $"d"$. If same block is attached to spring & released suddenly then maximum expansion in spring will be-

A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :