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Physics NEET Questions — Free MCQ Practice

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A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is:

A.

$5 (\hat{i} - 2 \hat{j})$

B.

$5 (4 \hat{i} + 2 \hat{j})$

C.

$0.6 \hat{i} + 0.8 \hat{j}$

D.

$6 \hat{i} + 8 \hat{j}$

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Explanation

$I n i t i a l p o s i t i o n (x_{1}, y_{1}) = (1, - 2) F i n a l p o s i t i o n (x_{2}, y_{2}) = (4, 2) D i s p l a c e m e n t = F i n a l p o s i t i o n - I n i t i a l p o s i t i o n = (x_{2} - x_{1}, y_{2} - y_{1}) = (3, 4) = 3 \hat{i} + 4 \hat{j} D i r e c t i o n o f v e l o c i t y i s s a m e a s d i p l a c e m e n t S o u n i t v e c t o r a l o n g d i s p l a c e m e n t = \frac{V e c t o r}{M a g n i t u d e} = \frac{3 \hat{i} + 4 \hat{j}}{\sqrt{3^{2} + 4^{2}}} = \frac{3 \hat{i} + 4 \hat{j}}{5} V e l o c i t y = M a g n i t u d e o f v e l o c i t y \times U n i t V e c t o r a l o n g v e l o c i t y = 10 \times (\frac{3 \hat{i} + 4 \hat{j}}{5}) = 6 \hat{i} + 8 \hat{j}$

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Which of the following is perpendicular to $\hat{i} - \hat{j} - \hat{k}$ ?

A.

$\hat{i} + \hat{j} + \hat{k}$

B.

$- \hat{i} + \hat{j} + \hat{k}$

C.

$\hat{i} + \hat{j} - \hat{k}$

D.

None of these

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Explanation

$I f v e c t o r \vec{A} i s ⊥ t o \vec{B,} \vec{B} . \vec{A} = 0 C h e c k i n g a l l o p t i o n s a) (\hat{i} - \hat{j} - \hat{k}) . (\hat{i} + \hat{j} + \hat{k}) = 1 - 1 - 1 = - 1 (N o t p e r p e n d i c u l a r) b) (\hat{i} - \hat{j} - \hat{k}) . (\hat{- i} + \hat{j} + \hat{k}) = - 1 - 1 - 1 = - 3 (N o t p e r p e n d i c u l a r) c) (\hat{i} - \hat{j} - \hat{k}) . (\hat{i} + \hat{j} - \hat{k}) = - 1 - 1 + 1 = 1 (N o t p e r p e n d i c u l a r) S o, n o o p t i o n m a t c h e s . A n s w e r i s o p t i o n D$

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Two constant forces $F_{1} = 2 \hat{i} - 3 \hat{j} + 3 \hat{k} (N)$ and $F_{2} = \hat{i} + \hat{j} - 2 \hat{k} (N)$ act on a body and displace it from the position $r_{1} = \hat{i} + 2 \hat{j} - 2 \hat{k} (m)$ to the position $r_{2} = 7 \hat{i} + 10 \hat{j} + 5 \hat{k} (m)$ . What is the work done?

A.

9 Joule

B.

41 Joule

C.

-3 Joule

D.

None of these

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Explanation

(A)

$Net force = {\vec{F}}_{1} + {\vec{F}}_{2} ({\vec{F}}_{net}) = (2 \hat{i} - 3 \hat{j} + 3 \hat{k}) + (\hat{i} + \hat{j} - 2 \hat{k}) = 3 \hat{i} - 2 \hat{j} + \hat{k} Displacement ∆ \vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1} = 6 \hat{i} + 8 \hat{j} + 7 \hat{k} Work done = Force . Displacement = {\vec{F}}_{net} . ∆ \vec{r} = (3 \hat{i} - 2 \hat{j} + \hat{k}) . (6 \hat{i} + 8 \hat{j} + 7 \hat{k}) = 18 - 16 + 7 = 9 J$

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The two vectors $A = 2 \hat{i} + \hat{j} + 3 \hat{k}$ and $B = 7 \hat{i} - 5 \hat{j} - 3 \hat{k}$ are -

A.

parallel

B.

perpendicular

C.

anti-parallel

D.

None of these

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Explanation

(B)

$\vec{A} . \vec{B} = 2 \times 7 + 1 \times (- 5) + 3 \times (- 3) = 14 - 5 - 9 = 0 \Rightarrow p e r p e n d i c u l a r$

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Two vectors $P = 2 \hat{i} + b \hat{j} + 2 \hat{k}$ and $Q = \hat{i} + \hat{j} + \hat{k}$ will be perpendicular if -

A.

b=0

B.

b=1

C.

b=2

D.

b=-4

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Explanation

$(D) F o r \vec{P} ⊥ \overset{}{\vec{Q}}, D o t p r o d u c t \vec{P} . \vec{Q} = 0 (2 \hat{i} + b j + 2 \hat{k}) . (\hat{i} + j + \hat{k}) = 0 2 + b + 2 = 0 b = - 4$

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A vector perpendicular to $(4 \hat{i} - 3 \hat{j})$ is -

A.

$4 \hat{i} + 3 \hat{j}$

B.

$7 \hat{k}$

C.

$6 \hat{i}$

D.

$3 \hat{i} - 4 \hat{j}$

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Explanation

(B) $(4 \hat{i} - 3 \hat{j}) . 7 \hat{k} = 0 S o \hat{k} i s t h e r e q u i r e d v e c t o r$

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Angle that the vector $A = 2 \hat{i} + 3 \hat{j}$ makes with y-axis is -

A.

$\tan^{- 1} 3 / 2$

B.

$\tan^{- 1} 2 / 3$

C.

$\sin^{- 1} 2 / 3$

D.

$\cos^{- 1} 3 / 2$

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Explanation

The angle that a vector makes with the y-axis is given by tan^-1(y/x). Here, the vector A = 2i + 3j has x = 2 and y = 3. Therefore, the angle it makes with the y-axis is tan^-1(3/2).

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A vector A points, vertically upward and, B points towards north. The vector product $A \times B$ is -

A.

along west

B.

along east

C.

zero

D.

vertically downward

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The linear velocity of a rotating body is given by $v = ω \times r$ , where $ω$ is the angular velocity and r is the radius vector. The angular velocity of a body $ω = \hat{i} - 2 \hat{j} + 2 \hat{k}$ and their radius vector $r = 4 \hat{j} - 3 \hat{k}, | v |$ is -

A.

$\sqrt{29} units$

B.

$31 units$

C.

$\sqrt{37} units$

D.

$\sqrt{41} units$

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Explanation

(A)

$\vec{V} = \vec{ω} \times \vec{r} = (\hat{i} - 2 \hat{j} + 2 \hat{k}) \times (4 \hat{j} - 3 \hat{k}) = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 2 & 2 \\ 0 & 4 & - 3 \end{matrix}| = (- 2 \times - 3 - 2 \times 4) \hat{i} + (1 \times - 3 - 2 \times 0) (- \hat{j}) + (1 \times 4 - (- 2) \times 0) \hat{k} \vec{V} = - 2 \hat{i} + 3 \hat{j} + 4 \hat{k} Magnitude of \vec{v}, |\vec{V}| = \sqrt{{(- 2)}^{2} + {(3)}^{2} + {(4)}^{2}} = \sqrt{29} units$

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The displacement x of a particle along a straight line at time t is given by $x = a_{0} + a_{1} t + a_{2} t^{2}$ . The acceleration of the particle is

A.

$a_{0}$

B.

$a_{1}$

C.

$2 a_{2}$

D.

$a_{2}$

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Explanation

(C)

$v = \frac{d x}{d t} = = a_{1} t^{1 - 1} + 2 a_{2} t^{2 - 1} = a_{1} + 2 a_{2} t a = \frac{d v}{d t} = 2 a_{2} t^{1 - 1} = 2 a_{2}$

Physics MCQs for NEET — Practice Questions with Answers

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