A vertical spring block system is made to oscillate.
Assertion (A): Its time period on earth is more than that on the moon.
Reason (R): Its extension on moon (in equilibrium) is more than that on the earth.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The time period of a vertical spring-block system is \(T = 2\pi \sqrt{\frac{m}{k}}\), which is independent of gravity (g). So (A) is false. The equilibrium extension is \(x_{eq} = \frac{mg}{k}\). Since \(g_{moon} < g_{earth}\), then \(x_{eq,moon} < x_{eq,earth}\). So (R) is also false.
Assertion (A): A spring block watch gives the correct time in orbiting satellite.
Reason (R): Time period of a spring block watch is independent of \(g\) and depends only on spring factor and mass of the block.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The time period of a spring-mass system is \(T = 2\pi \sqrt{m/k}\). This equation shows that the time period is independent of the acceleration due to gravity \(g\). Therefore, a spring block watch would function correctly in an orbiting satellite where effective \(g\) is zero. Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
Assertion (A): The periodic time of a hard spring is less as compared to that of a soft spring.
Reason (R): The spring constant is large for hard spring.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The periodic time of a spring is given by `\(T = 2\pi\sqrt{\frac{m}{k}}\)`.
A hard spring has a large spring constant `\(k\)`, which means a smaller `\(T\)`. A soft spring has a small `\(k\)`, hence a larger `\(T\)`. Both A and R are true, and R explains A.