(A) The magnitude of the force vector $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k}$ is calculated as:$|\vec{F}| = \sqrt{(6)^2 + (-8)^2 + (10)^2} = \sqrt

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(A) The magnitude of the force vector $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k}$ is calculated as:$|\vec{F}| = \sqrt{(6)^2 + (-8)^2 + (10)^2} = \sqrt{36 + 64 + 100} = \sqrt{200} \, N$.Using Newton's second law of motion,$F = ma$,where $a = 1 \, m/s^2$:$m = \frac{F}{a} = \frac{\sqrt{200}}{1} = \sqrt{100 \times 2} = 10\sqrt{2} \, kg$.Therefore,the mass of the body is $10\sqrt{2} \, kg$.

Class 11 Physics Newton's Laws of Motion and Friction Second Law of Motion

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$A$ force vector applied on a mass is represented as $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k} \, N$ and it accelerates with $1 \, m/s^2$. What will be the mass of the body?

A
$10\sqrt{2} \, kg$
B
$2\sqrt{10} \, kg$
C
$10 \, kg$
D
$20 \, kg$

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Class 11

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Newton's Laws of Motion and Friction

Subtopic

Second Law of Motion

$A$ particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$-direction. Its speed $v(t)$ is depicted by which of the following curves?

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$A$ body of mass $2 \, kg$ is moving with a velocity $8 \, m/s$ on a smooth surface. If it is to be brought to rest in $4 \, seconds$,then the force to be applied is ......... $N$.

Easy

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$A$ cricket ball of mass $50 \ g$ having velocity $50 \ cm \ s^{-1}$ is stopped in $0.5 \ s$. The force applied to stop the ball is (in $N$)

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When a body is acted upon by a constant force,then which of the following quantities remains constant?

Easy

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If a bullet of mass $5 \,g$ moving with velocity $100 \,m/s$ penetrates a wooden block up to $6 \,cm$,then the average force imposed by the bullet on the block is ........... $N$.

Medium

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$A$ force vector applied on a mass is represented as $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k} \, N$ and it accelerates with $1 \, m/s^2$. What will be the mass of the body?

Similar Questions

$A$ particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$-direction. Its speed $v(t)$ is depicted by which of the following curves?

$A$ body of mass $2 \, kg$ is moving with a velocity $8 \, m/s$ on a smooth surface. If it is to be brought to rest in $4 \, seconds$,then the force to be applied is ......... $N$.

$A$ cricket ball of mass $50 \ g$ having velocity $50 \ cm \ s^{-1}$ is stopped in $0.5 \ s$. The force applied to stop the ball is (in $N$)

When a body is acted upon by a constant force,then which of the following quantities remains constant?

If a bullet of mass $5 \,g$ moving with velocity $100 \,m/s$ penetrates a wooden block up to $6 \,cm$,then the average force imposed by the bullet on the block is ........... $N$.

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