Magnitude using Vector: Derivation

Q. An object of $60\text{kg-wt}$ is weighed by hanging it to the spring balance, from the ceiling of a car. If the car starts moving around a curve of radius $10\text{m}$ at a speed $10{\text{ms}}^{-1}$. The reading of the spring balance would be
[$1\text{kg-wt}=10\text{N}$]

1. $60\sqrt{2}\text{kg-wt}$
2. $60\text{kg-wt}$
3. $120\sqrt{2}\text{kg-wt}$
4. $600\text{kg-wt}$

Q. Th figure shows a block of mass $m$ moving without friction along three tracks with same speed $v$.

Choose the correct relation

1. $N_1>N_2$
2. $N_2>N_3$
3. $N_3>N_1$
4. $N_1=N_2=N_3$

Q. A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5\text{m/s}$. What is the height of the plane of circle from vertex of the funnel?

1. $0.25\text{cm}$
2. $2\text{cm}$
3. $0.025\text{cm}$
4. $2.5\text{cm}$

Q. In a uniform circular motion, the formula $a={\omega }^{2}r$ gives magnitude of acceleration.

1. tangential
2. centripetal
3. no

Q. A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. The value of $x$ for point $P$, where tension is ${\left(\frac{1}{4}\right)}^{th}$ of the tension at $O$

1. $\frac{L}{2}$
2. $\frac{L}{4}$
3. $\frac{3L}{4}$
4. $\frac{\sqrt{3}L}{2}$

Q. A ball of mass $0.25\text{kg}$ attached to the string of length $1.96\text{m}$ is moving in a horizontal circle. The string will break if the tension in the string is more than $25\text{N}$. What is the maximum angular velocity with which the ball can be moved?

1. $7.14\text{rad/s}$
2. $3.92\text{rad/s}$
3. $1.57\text{rad/s}$
4. $14.28\text{rad/s}$

Q. A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. The value of $x$ for point $P$, where tension is ${\left(\frac{1}{4}\right)}^{th}$ of the tension at $O$

1. $\frac{L}{2}$
2. $\frac{L}{4}$
3. $\frac{3L}{4}$
4. $\frac{\sqrt{3}L}{2}$