366204
If the direction of position vector \(\vec{r}\) is towards south and direction of force vector \(\vec{F}\) is towards east, then the direction of torque vector \(\vec{\tau}\) is
1 Towards north
2 Towards west
3 Vertically upward
4 Vertically downward
Explanation:
Apply right hand thumb rule for \(\vec{\tau}=\vec{r} \times \vec{F}\) The direction of \(\vec{\tau}\) is in upward direction.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366205
The force \(7 \hat{i}+3 \hat{j}-5 \hat{k}\) acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}\). What is the torque of a given force about the origin?
366206
Assertion : To unscrew a rusted nut, we need a wrench with longer arm. Reason : Wrench with longer arm reduces the torque of the arm.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
We know \(\tau=r \times F\) To unscrew a rusted nut, a wrench with a longer arm \((r)\) is needed to provide more torque. The reason is also true; a wrench with a longer arm increases the lever arm, which reduces the amount of force \((F)\) needed to produce the same torque. So correct option is (1).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366207
A force \(F\) is applied on a single particle \(P\) as shown in the figure. Here, \(r\) is the position vector of the particle. The value of torque \(\tau\) is
1 \(Fr\)
2 \(r F \sin \theta\)
3 \(r F \tan \theta\)
4 \(r F \cos \theta\)
Explanation:
The moment of the force acting on the particle with respect to the origin \(O\) is defined as the vector product. \(\vec{\tau}=\vec{r} \times \vec{F} \Rightarrow|\tau|=r F \sin \theta\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366208
Find the torque about the origin when a force of \(3\hat j\;N\) acts on a particle whose position vector is \(2\,km\).
1 \(6\hat j\,Nm\)
2 \( - 6\hat i\,Nm\)
3 \(6\hat k\,Nm\)
4 \(6\hat i\,Nm\)
Explanation:
\(\vec F = 3\hat jN,\,\,\vec r = 2\hat k\,\,\) \(\,\vec \tau = \vec r \times \vec F = 2\hat k \times 3\hat j{\rm{ }} = 6(\hat k \times \hat j)\) \( = 6( - \hat i)\) \(\vec \tau {\rm{ }} = - 6\hat iNm\)
366204
If the direction of position vector \(\vec{r}\) is towards south and direction of force vector \(\vec{F}\) is towards east, then the direction of torque vector \(\vec{\tau}\) is
1 Towards north
2 Towards west
3 Vertically upward
4 Vertically downward
Explanation:
Apply right hand thumb rule for \(\vec{\tau}=\vec{r} \times \vec{F}\) The direction of \(\vec{\tau}\) is in upward direction.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366205
The force \(7 \hat{i}+3 \hat{j}-5 \hat{k}\) acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}\). What is the torque of a given force about the origin?
366206
Assertion : To unscrew a rusted nut, we need a wrench with longer arm. Reason : Wrench with longer arm reduces the torque of the arm.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
We know \(\tau=r \times F\) To unscrew a rusted nut, a wrench with a longer arm \((r)\) is needed to provide more torque. The reason is also true; a wrench with a longer arm increases the lever arm, which reduces the amount of force \((F)\) needed to produce the same torque. So correct option is (1).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366207
A force \(F\) is applied on a single particle \(P\) as shown in the figure. Here, \(r\) is the position vector of the particle. The value of torque \(\tau\) is
1 \(Fr\)
2 \(r F \sin \theta\)
3 \(r F \tan \theta\)
4 \(r F \cos \theta\)
Explanation:
The moment of the force acting on the particle with respect to the origin \(O\) is defined as the vector product. \(\vec{\tau}=\vec{r} \times \vec{F} \Rightarrow|\tau|=r F \sin \theta\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366208
Find the torque about the origin when a force of \(3\hat j\;N\) acts on a particle whose position vector is \(2\,km\).
1 \(6\hat j\,Nm\)
2 \( - 6\hat i\,Nm\)
3 \(6\hat k\,Nm\)
4 \(6\hat i\,Nm\)
Explanation:
\(\vec F = 3\hat jN,\,\,\vec r = 2\hat k\,\,\) \(\,\vec \tau = \vec r \times \vec F = 2\hat k \times 3\hat j{\rm{ }} = 6(\hat k \times \hat j)\) \( = 6( - \hat i)\) \(\vec \tau {\rm{ }} = - 6\hat iNm\)
366204
If the direction of position vector \(\vec{r}\) is towards south and direction of force vector \(\vec{F}\) is towards east, then the direction of torque vector \(\vec{\tau}\) is
1 Towards north
2 Towards west
3 Vertically upward
4 Vertically downward
Explanation:
Apply right hand thumb rule for \(\vec{\tau}=\vec{r} \times \vec{F}\) The direction of \(\vec{\tau}\) is in upward direction.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366205
The force \(7 \hat{i}+3 \hat{j}-5 \hat{k}\) acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}\). What is the torque of a given force about the origin?
366206
Assertion : To unscrew a rusted nut, we need a wrench with longer arm. Reason : Wrench with longer arm reduces the torque of the arm.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
We know \(\tau=r \times F\) To unscrew a rusted nut, a wrench with a longer arm \((r)\) is needed to provide more torque. The reason is also true; a wrench with a longer arm increases the lever arm, which reduces the amount of force \((F)\) needed to produce the same torque. So correct option is (1).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366207
A force \(F\) is applied on a single particle \(P\) as shown in the figure. Here, \(r\) is the position vector of the particle. The value of torque \(\tau\) is
1 \(Fr\)
2 \(r F \sin \theta\)
3 \(r F \tan \theta\)
4 \(r F \cos \theta\)
Explanation:
The moment of the force acting on the particle with respect to the origin \(O\) is defined as the vector product. \(\vec{\tau}=\vec{r} \times \vec{F} \Rightarrow|\tau|=r F \sin \theta\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366208
Find the torque about the origin when a force of \(3\hat j\;N\) acts on a particle whose position vector is \(2\,km\).
1 \(6\hat j\,Nm\)
2 \( - 6\hat i\,Nm\)
3 \(6\hat k\,Nm\)
4 \(6\hat i\,Nm\)
Explanation:
\(\vec F = 3\hat jN,\,\,\vec r = 2\hat k\,\,\) \(\,\vec \tau = \vec r \times \vec F = 2\hat k \times 3\hat j{\rm{ }} = 6(\hat k \times \hat j)\) \( = 6( - \hat i)\) \(\vec \tau {\rm{ }} = - 6\hat iNm\)
366204
If the direction of position vector \(\vec{r}\) is towards south and direction of force vector \(\vec{F}\) is towards east, then the direction of torque vector \(\vec{\tau}\) is
1 Towards north
2 Towards west
3 Vertically upward
4 Vertically downward
Explanation:
Apply right hand thumb rule for \(\vec{\tau}=\vec{r} \times \vec{F}\) The direction of \(\vec{\tau}\) is in upward direction.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366205
The force \(7 \hat{i}+3 \hat{j}-5 \hat{k}\) acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}\). What is the torque of a given force about the origin?
366206
Assertion : To unscrew a rusted nut, we need a wrench with longer arm. Reason : Wrench with longer arm reduces the torque of the arm.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
We know \(\tau=r \times F\) To unscrew a rusted nut, a wrench with a longer arm \((r)\) is needed to provide more torque. The reason is also true; a wrench with a longer arm increases the lever arm, which reduces the amount of force \((F)\) needed to produce the same torque. So correct option is (1).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366207
A force \(F\) is applied on a single particle \(P\) as shown in the figure. Here, \(r\) is the position vector of the particle. The value of torque \(\tau\) is
1 \(Fr\)
2 \(r F \sin \theta\)
3 \(r F \tan \theta\)
4 \(r F \cos \theta\)
Explanation:
The moment of the force acting on the particle with respect to the origin \(O\) is defined as the vector product. \(\vec{\tau}=\vec{r} \times \vec{F} \Rightarrow|\tau|=r F \sin \theta\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366208
Find the torque about the origin when a force of \(3\hat j\;N\) acts on a particle whose position vector is \(2\,km\).
1 \(6\hat j\,Nm\)
2 \( - 6\hat i\,Nm\)
3 \(6\hat k\,Nm\)
4 \(6\hat i\,Nm\)
Explanation:
\(\vec F = 3\hat jN,\,\,\vec r = 2\hat k\,\,\) \(\,\vec \tau = \vec r \times \vec F = 2\hat k \times 3\hat j{\rm{ }} = 6(\hat k \times \hat j)\) \( = 6( - \hat i)\) \(\vec \tau {\rm{ }} = - 6\hat iNm\)
366204
If the direction of position vector \(\vec{r}\) is towards south and direction of force vector \(\vec{F}\) is towards east, then the direction of torque vector \(\vec{\tau}\) is
1 Towards north
2 Towards west
3 Vertically upward
4 Vertically downward
Explanation:
Apply right hand thumb rule for \(\vec{\tau}=\vec{r} \times \vec{F}\) The direction of \(\vec{\tau}\) is in upward direction.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366205
The force \(7 \hat{i}+3 \hat{j}-5 \hat{k}\) acts on a particle whose position vector is \(\hat{i}-\hat{j}+\hat{k}\). What is the torque of a given force about the origin?
366206
Assertion : To unscrew a rusted nut, we need a wrench with longer arm. Reason : Wrench with longer arm reduces the torque of the arm.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
We know \(\tau=r \times F\) To unscrew a rusted nut, a wrench with a longer arm \((r)\) is needed to provide more torque. The reason is also true; a wrench with a longer arm increases the lever arm, which reduces the amount of force \((F)\) needed to produce the same torque. So correct option is (1).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366207
A force \(F\) is applied on a single particle \(P\) as shown in the figure. Here, \(r\) is the position vector of the particle. The value of torque \(\tau\) is
1 \(Fr\)
2 \(r F \sin \theta\)
3 \(r F \tan \theta\)
4 \(r F \cos \theta\)
Explanation:
The moment of the force acting on the particle with respect to the origin \(O\) is defined as the vector product. \(\vec{\tau}=\vec{r} \times \vec{F} \Rightarrow|\tau|=r F \sin \theta\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366208
Find the torque about the origin when a force of \(3\hat j\;N\) acts on a particle whose position vector is \(2\,km\).
1 \(6\hat j\,Nm\)
2 \( - 6\hat i\,Nm\)
3 \(6\hat k\,Nm\)
4 \(6\hat i\,Nm\)
Explanation:
\(\vec F = 3\hat jN,\,\,\vec r = 2\hat k\,\,\) \(\,\vec \tau = \vec r \times \vec F = 2\hat k \times 3\hat j{\rm{ }} = 6(\hat k \times \hat j)\) \( = 6( - \hat i)\) \(\vec \tau {\rm{ }} = - 6\hat iNm\)
