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
Explanation:
When a force of constant magnitude is perpendicular to the velocity of particle acts on, work done is zero and hence change in kinetic energy is zero.
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 \(\left| {\hat i} \right| = 1\) and \(\left| {\hat j} \right| = 1\). Magnitude of resultant vector is equal to \(\sqrt {{{\left| {\hat i} \right|}^2} + {{\left| {\hat j} \right|}^2}} = \sqrt {{{(1)}^2} + {{( - 1)}^2}} = \sqrt 2 \)
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. \(\therefore u\cos \alpha \times t = d\) \( \Rightarrow t = \frac{d}{{u \times \frac{d}{{\sqrt {h + {d^2}} }}}} = \frac{{\sqrt {{h^2} + {d^2}} }}{u}\) \(\therefore {y_s} = u\sin \alpha \times t - \frac{1}{2}g{t^2}\) \( = u \times \frac{h}{{\sqrt {{h^2} + {d^2}} }} - \frac{g}{2} \times \frac{{{h^2} + {d^2}}}{{{u^2}}}\) \( \Rightarrow {y_s} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_f} = h - \frac{1}{2}g{t^2} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_s}\, = \,{y_f}\) the stone always hits the fruit
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. \(\therefore \,\,\,\,\vec v = \mathop {\lim }\limits_{\Delta t \to 0} \,\frac{{\Delta \vec r}}{{\Delta t}} = \frac{{d\vec r}}{{dt}}\) The direction of \({\vec v}\) and \(\frac{{\Delta \vec r}}{{\Delta t}}\) is same.
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
Explanation:
When a force of constant magnitude is perpendicular to the velocity of particle acts on, work done is zero and hence change in kinetic energy is zero.
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 \(\left| {\hat i} \right| = 1\) and \(\left| {\hat j} \right| = 1\). Magnitude of resultant vector is equal to \(\sqrt {{{\left| {\hat i} \right|}^2} + {{\left| {\hat j} \right|}^2}} = \sqrt {{{(1)}^2} + {{( - 1)}^2}} = \sqrt 2 \)
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. \(\therefore u\cos \alpha \times t = d\) \( \Rightarrow t = \frac{d}{{u \times \frac{d}{{\sqrt {h + {d^2}} }}}} = \frac{{\sqrt {{h^2} + {d^2}} }}{u}\) \(\therefore {y_s} = u\sin \alpha \times t - \frac{1}{2}g{t^2}\) \( = u \times \frac{h}{{\sqrt {{h^2} + {d^2}} }} - \frac{g}{2} \times \frac{{{h^2} + {d^2}}}{{{u^2}}}\) \( \Rightarrow {y_s} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_f} = h - \frac{1}{2}g{t^2} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_s}\, = \,{y_f}\) the stone always hits the fruit
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. \(\therefore \,\,\,\,\vec v = \mathop {\lim }\limits_{\Delta t \to 0} \,\frac{{\Delta \vec r}}{{\Delta t}} = \frac{{d\vec r}}{{dt}}\) The direction of \({\vec v}\) and \(\frac{{\Delta \vec r}}{{\Delta t}}\) is same.
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
Explanation:
When a force of constant magnitude is perpendicular to the velocity of particle acts on, work done is zero and hence change in kinetic energy is zero.
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 \(\left| {\hat i} \right| = 1\) and \(\left| {\hat j} \right| = 1\). Magnitude of resultant vector is equal to \(\sqrt {{{\left| {\hat i} \right|}^2} + {{\left| {\hat j} \right|}^2}} = \sqrt {{{(1)}^2} + {{( - 1)}^2}} = \sqrt 2 \)
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. \(\therefore u\cos \alpha \times t = d\) \( \Rightarrow t = \frac{d}{{u \times \frac{d}{{\sqrt {h + {d^2}} }}}} = \frac{{\sqrt {{h^2} + {d^2}} }}{u}\) \(\therefore {y_s} = u\sin \alpha \times t - \frac{1}{2}g{t^2}\) \( = u \times \frac{h}{{\sqrt {{h^2} + {d^2}} }} - \frac{g}{2} \times \frac{{{h^2} + {d^2}}}{{{u^2}}}\) \( \Rightarrow {y_s} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_f} = h - \frac{1}{2}g{t^2} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_s}\, = \,{y_f}\) the stone always hits the fruit
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. \(\therefore \,\,\,\,\vec v = \mathop {\lim }\limits_{\Delta t \to 0} \,\frac{{\Delta \vec r}}{{\Delta t}} = \frac{{d\vec r}}{{dt}}\) The direction of \({\vec v}\) and \(\frac{{\Delta \vec r}}{{\Delta t}}\) is same.
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
Explanation:
When a force of constant magnitude is perpendicular to the velocity of particle acts on, work done is zero and hence change in kinetic energy is zero.
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 \(\left| {\hat i} \right| = 1\) and \(\left| {\hat j} \right| = 1\). Magnitude of resultant vector is equal to \(\sqrt {{{\left| {\hat i} \right|}^2} + {{\left| {\hat j} \right|}^2}} = \sqrt {{{(1)}^2} + {{( - 1)}^2}} = \sqrt 2 \)
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. \(\therefore u\cos \alpha \times t = d\) \( \Rightarrow t = \frac{d}{{u \times \frac{d}{{\sqrt {h + {d^2}} }}}} = \frac{{\sqrt {{h^2} + {d^2}} }}{u}\) \(\therefore {y_s} = u\sin \alpha \times t - \frac{1}{2}g{t^2}\) \( = u \times \frac{h}{{\sqrt {{h^2} + {d^2}} }} - \frac{g}{2} \times \frac{{{h^2} + {d^2}}}{{{u^2}}}\) \( \Rightarrow {y_s} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_f} = h - \frac{1}{2}g{t^2} = h - \frac{{g\left( {{h^2} + {d^2}} \right)}}{{2{u^2}}}\) and \({y_s}\, = \,{y_f}\) the stone always hits the fruit
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. \(\therefore \,\,\,\,\vec v = \mathop {\lim }\limits_{\Delta t \to 0} \,\frac{{\Delta \vec r}}{{\Delta t}} = \frac{{d\vec r}}{{dt}}\) The direction of \({\vec v}\) and \(\frac{{\Delta \vec r}}{{\Delta t}}\) is same.
