QBManager

PHXI04:MOTION IN A PLANE

361920 A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

1 Its velocity is constant

2 Its acceleration is constant

3 Its kinetic energy is constant

4 It moves in a straight line

PHXI04:MOTION IN A PLANE

361921 Statement A :
If $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ -axis and $y$ -axis respectively, the magnitude of vector $\hat{i} - \hat{j}$ will be $\sqrt{2}$ .
Statement B :
Unit vectors are used to indicate direction only.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

Since $\hat{i}$ and $\hat{j}$ are unit vectors, their magnitude are $| \hat{i} | = 1$ and $| \hat{j} | = 1$ . Magnitude of resultant vector is equal to
$\sqrt{{| \hat{i} |}^{2} + {| \hat{j} |}^{2}} = \sqrt{{(1)}^{2} + {(- 1)}^{2}} = \sqrt{2}$

PHXI04:MOTION IN A PLANE

361922 A person standing at some distance from a high tree, throws a stone taking aim at a fruit hanging from that tree. The fruit begins to fall freely at the time when the person throws the stone. Correct statement among the following is

1 The stone moves above the falling fruit.

2 The stone strikes the fruit if the stone is thrown with a definite velocity.

3 The stone moves below the falling fruit.

4 The stone always hits the fruit.

Explanation:

Let after time $t, y_{s}$ and $y_{f}$ be respective heights of stone and fruit.
$∴ u \cos α \times t = d$
$\Rightarrow t = \frac{d}{u \times \frac{d}{\sqrt{h + d^{2}}}} = \frac{\sqrt{h^{2} + d^{2}}}{u}$
$∴ y_{s} = u \sin α \times t - \frac{1}{2} g t^{2}$
$= u \times \frac{h}{\sqrt{h^{2} + d^{2}}} - \frac{g}{2} \times \frac{h^{2} + d^{2}}{u^{2}}$
$\Rightarrow y_{s} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{f} = h - \frac{1}{2} g t^{2} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{s} = y_{f}$ the stone always hits the fruit
supporting img

PHXI04:MOTION IN A PLANE

361923 Statement A :
The instantaneous velocity is given by the limiting value of the average velocity as the time interval approaches zero.
Statement B :
The direction of the average velocity is same as that of displacement.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

The instantaneous velocity is the limiting value of the average velocity as the time interval approaches zero.
$∴ \vec{v} = lim_{Δ t \to 0} \frac{Δ \vec{r}}{Δ t} = \frac{d \vec{r}}{d t}$
The direction of $\vec{v}$ and $\frac{Δ \vec{r}}{Δ t}$ is same.
supporting img

PHXI04:MOTION IN A PLANE

361920 A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

1 Its velocity is constant

2 Its acceleration is constant

3 Its kinetic energy is constant

4 It moves in a straight line

PHXI04:MOTION IN A PLANE

361921 Statement A :
If $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ -axis and $y$ -axis respectively, the magnitude of vector $\hat{i} - \hat{j}$ will be $\sqrt{2}$ .
Statement B :
Unit vectors are used to indicate direction only.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

Since $\hat{i}$ and $\hat{j}$ are unit vectors, their magnitude are $| \hat{i} | = 1$ and $| \hat{j} | = 1$ . Magnitude of resultant vector is equal to
$\sqrt{{| \hat{i} |}^{2} + {| \hat{j} |}^{2}} = \sqrt{{(1)}^{2} + {(- 1)}^{2}} = \sqrt{2}$

PHXI04:MOTION IN A PLANE

361922 A person standing at some distance from a high tree, throws a stone taking aim at a fruit hanging from that tree. The fruit begins to fall freely at the time when the person throws the stone. Correct statement among the following is

1 The stone moves above the falling fruit.

2 The stone strikes the fruit if the stone is thrown with a definite velocity.

3 The stone moves below the falling fruit.

4 The stone always hits the fruit.

Explanation:

Let after time $t, y_{s}$ and $y_{f}$ be respective heights of stone and fruit.
$∴ u \cos α \times t = d$
$\Rightarrow t = \frac{d}{u \times \frac{d}{\sqrt{h + d^{2}}}} = \frac{\sqrt{h^{2} + d^{2}}}{u}$
$∴ y_{s} = u \sin α \times t - \frac{1}{2} g t^{2}$
$= u \times \frac{h}{\sqrt{h^{2} + d^{2}}} - \frac{g}{2} \times \frac{h^{2} + d^{2}}{u^{2}}$
$\Rightarrow y_{s} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{f} = h - \frac{1}{2} g t^{2} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{s} = y_{f}$ the stone always hits the fruit
supporting img

PHXI04:MOTION IN A PLANE

361923 Statement A :
The instantaneous velocity is given by the limiting value of the average velocity as the time interval approaches zero.
Statement B :
The direction of the average velocity is same as that of displacement.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

The instantaneous velocity is the limiting value of the average velocity as the time interval approaches zero.
$∴ \vec{v} = lim_{Δ t \to 0} \frac{Δ \vec{r}}{Δ t} = \frac{d \vec{r}}{d t}$
The direction of $\vec{v}$ and $\frac{Δ \vec{r}}{Δ t}$ is same.
supporting img

PHXI04:MOTION IN A PLANE

361920 A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

1 Its velocity is constant

2 Its acceleration is constant

3 Its kinetic energy is constant

4 It moves in a straight line

PHXI04:MOTION IN A PLANE

361921 Statement A :
If $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ -axis and $y$ -axis respectively, the magnitude of vector $\hat{i} - \hat{j}$ will be $\sqrt{2}$ .
Statement B :
Unit vectors are used to indicate direction only.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

Since $\hat{i}$ and $\hat{j}$ are unit vectors, their magnitude are $| \hat{i} | = 1$ and $| \hat{j} | = 1$ . Magnitude of resultant vector is equal to
$\sqrt{{| \hat{i} |}^{2} + {| \hat{j} |}^{2}} = \sqrt{{(1)}^{2} + {(- 1)}^{2}} = \sqrt{2}$

PHXI04:MOTION IN A PLANE

361922 A person standing at some distance from a high tree, throws a stone taking aim at a fruit hanging from that tree. The fruit begins to fall freely at the time when the person throws the stone. Correct statement among the following is

1 The stone moves above the falling fruit.

2 The stone strikes the fruit if the stone is thrown with a definite velocity.

3 The stone moves below the falling fruit.

4 The stone always hits the fruit.

Explanation:

Let after time $t, y_{s}$ and $y_{f}$ be respective heights of stone and fruit.
$∴ u \cos α \times t = d$
$\Rightarrow t = \frac{d}{u \times \frac{d}{\sqrt{h + d^{2}}}} = \frac{\sqrt{h^{2} + d^{2}}}{u}$
$∴ y_{s} = u \sin α \times t - \frac{1}{2} g t^{2}$
$= u \times \frac{h}{\sqrt{h^{2} + d^{2}}} - \frac{g}{2} \times \frac{h^{2} + d^{2}}{u^{2}}$
$\Rightarrow y_{s} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{f} = h - \frac{1}{2} g t^{2} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{s} = y_{f}$ the stone always hits the fruit
supporting img

PHXI04:MOTION IN A PLANE

361923 Statement A :
The instantaneous velocity is given by the limiting value of the average velocity as the time interval approaches zero.
Statement B :
The direction of the average velocity is same as that of displacement.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

The instantaneous velocity is the limiting value of the average velocity as the time interval approaches zero.
$∴ \vec{v} = lim_{Δ t \to 0} \frac{Δ \vec{r}}{Δ t} = \frac{d \vec{r}}{d t}$
The direction of $\vec{v}$ and $\frac{Δ \vec{r}}{Δ t}$ is same.
supporting img

PHXI04:MOTION IN A PLANE

361920 A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

1 Its velocity is constant

2 Its acceleration is constant

3 Its kinetic energy is constant

4 It moves in a straight line

PHXI04:MOTION IN A PLANE

361921 Statement A :
If $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ -axis and $y$ -axis respectively, the magnitude of vector $\hat{i} - \hat{j}$ will be $\sqrt{2}$ .
Statement B :
Unit vectors are used to indicate direction only.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

Since $\hat{i}$ and $\hat{j}$ are unit vectors, their magnitude are $| \hat{i} | = 1$ and $| \hat{j} | = 1$ . Magnitude of resultant vector is equal to
$\sqrt{{| \hat{i} |}^{2} + {| \hat{j} |}^{2}} = \sqrt{{(1)}^{2} + {(- 1)}^{2}} = \sqrt{2}$

PHXI04:MOTION IN A PLANE

361922 A person standing at some distance from a high tree, throws a stone taking aim at a fruit hanging from that tree. The fruit begins to fall freely at the time when the person throws the stone. Correct statement among the following is

1 The stone moves above the falling fruit.

2 The stone strikes the fruit if the stone is thrown with a definite velocity.

3 The stone moves below the falling fruit.

4 The stone always hits the fruit.

Explanation:

Let after time $t, y_{s}$ and $y_{f}$ be respective heights of stone and fruit.
$∴ u \cos α \times t = d$
$\Rightarrow t = \frac{d}{u \times \frac{d}{\sqrt{h + d^{2}}}} = \frac{\sqrt{h^{2} + d^{2}}}{u}$
$∴ y_{s} = u \sin α \times t - \frac{1}{2} g t^{2}$
$= u \times \frac{h}{\sqrt{h^{2} + d^{2}}} - \frac{g}{2} \times \frac{h^{2} + d^{2}}{u^{2}}$
$\Rightarrow y_{s} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{f} = h - \frac{1}{2} g t^{2} = h - \frac{g (h^{2} + d^{2})}{2 u^{2}}$
and $y_{s} = y_{f}$ the stone always hits the fruit
supporting img

PHXI04:MOTION IN A PLANE

361923 Statement A :
The instantaneous velocity is given by the limiting value of the average velocity as the time interval approaches zero.
Statement B :
The direction of the average velocity is same as that of displacement.

1 Statement A is correct but Statement B is incorrect.

2 Statement A is incorrect but Statement B is correct.

3 Both Statements are correct.

4 Both Statements are incorrect.

Explanation:

The instantaneous velocity is the limiting value of the average velocity as the time interval approaches zero.
$∴ \vec{v} = lim_{Δ t \to 0} \frac{Δ \vec{r}}{Δ t} = \frac{d \vec{r}}{d t}$
The direction of $\vec{v}$ and $\frac{Δ \vec{r}}{Δ t}$ is same.
supporting img