04. Circular Motion : Uniform Circular Motion, Dynamic Circular Motion
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Motion in Plane

144026 A particle tied to a string of negligible weight and length \(l\) is swinging in a horizontal circular path with constant angular velocity having time period \(T\). If the string length is shortened by \(\frac{l}{2}\), while the particle is in motion, the period is:

1 \(4 \mathrm{~T}\)
2 \(2 \mathrm{~T}\)
3 \(\mathrm{T}\)
4 \(\frac{T}{4}\)
Motion in Plane

144027 A child starts running from rest along a circular track of radius ' \(r\) ' with constant tangential acceleration ' \(a\) '. After time ' \(t\) ' he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]}{r g}\)
2 \(\frac{\left[a^{2} t^{2}+a^{2} r^{4}\right]}{r g}\)
3 \(\frac{\left[a^{4} t^{4}-a^{2} r^{2}\right]^{\frac{1}{2}}}{r g}\)
4 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]^{\frac{1}{2}}}{g r}\)
Motion in Plane

144028 A body is moving along a circular track of radius \(100 \mathrm{~m}\) with velocity \(20 \mathrm{~m} / \mathrm{s}\). Its tangential acceleration is \(3 \mathrm{~m} / \mathrm{s}^{2}\), then its resultant acceleration will be

1 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(3 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144030 A bucket containing water is revolved in a vertical circle of radius ' \(r\) '. To prevent the water from falling down, the minimum frequency of revolution required is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{1}{2 \pi} \sqrt{\frac{\mathrm{r}}{\mathrm{g}}}\)
2 \(2 \pi \sqrt{\frac{g}{r}}\)
3 \(\frac{1}{2 \pi} \sqrt{\frac{g}{r}}\)
4 \(\frac{2 \pi g}{r}\)
Motion in Plane

144026 A particle tied to a string of negligible weight and length \(l\) is swinging in a horizontal circular path with constant angular velocity having time period \(T\). If the string length is shortened by \(\frac{l}{2}\), while the particle is in motion, the period is:

1 \(4 \mathrm{~T}\)
2 \(2 \mathrm{~T}\)
3 \(\mathrm{T}\)
4 \(\frac{T}{4}\)
Motion in Plane

144027 A child starts running from rest along a circular track of radius ' \(r\) ' with constant tangential acceleration ' \(a\) '. After time ' \(t\) ' he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]}{r g}\)
2 \(\frac{\left[a^{2} t^{2}+a^{2} r^{4}\right]}{r g}\)
3 \(\frac{\left[a^{4} t^{4}-a^{2} r^{2}\right]^{\frac{1}{2}}}{r g}\)
4 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]^{\frac{1}{2}}}{g r}\)
Motion in Plane

144028 A body is moving along a circular track of radius \(100 \mathrm{~m}\) with velocity \(20 \mathrm{~m} / \mathrm{s}\). Its tangential acceleration is \(3 \mathrm{~m} / \mathrm{s}^{2}\), then its resultant acceleration will be

1 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(3 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144030 A bucket containing water is revolved in a vertical circle of radius ' \(r\) '. To prevent the water from falling down, the minimum frequency of revolution required is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{1}{2 \pi} \sqrt{\frac{\mathrm{r}}{\mathrm{g}}}\)
2 \(2 \pi \sqrt{\frac{g}{r}}\)
3 \(\frac{1}{2 \pi} \sqrt{\frac{g}{r}}\)
4 \(\frac{2 \pi g}{r}\)
Motion in Plane

144026 A particle tied to a string of negligible weight and length \(l\) is swinging in a horizontal circular path with constant angular velocity having time period \(T\). If the string length is shortened by \(\frac{l}{2}\), while the particle is in motion, the period is:

1 \(4 \mathrm{~T}\)
2 \(2 \mathrm{~T}\)
3 \(\mathrm{T}\)
4 \(\frac{T}{4}\)
Motion in Plane

144027 A child starts running from rest along a circular track of radius ' \(r\) ' with constant tangential acceleration ' \(a\) '. After time ' \(t\) ' he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]}{r g}\)
2 \(\frac{\left[a^{2} t^{2}+a^{2} r^{4}\right]}{r g}\)
3 \(\frac{\left[a^{4} t^{4}-a^{2} r^{2}\right]^{\frac{1}{2}}}{r g}\)
4 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]^{\frac{1}{2}}}{g r}\)
Motion in Plane

144028 A body is moving along a circular track of radius \(100 \mathrm{~m}\) with velocity \(20 \mathrm{~m} / \mathrm{s}\). Its tangential acceleration is \(3 \mathrm{~m} / \mathrm{s}^{2}\), then its resultant acceleration will be

1 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(3 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144030 A bucket containing water is revolved in a vertical circle of radius ' \(r\) '. To prevent the water from falling down, the minimum frequency of revolution required is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{1}{2 \pi} \sqrt{\frac{\mathrm{r}}{\mathrm{g}}}\)
2 \(2 \pi \sqrt{\frac{g}{r}}\)
3 \(\frac{1}{2 \pi} \sqrt{\frac{g}{r}}\)
4 \(\frac{2 \pi g}{r}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Motion in Plane

144026 A particle tied to a string of negligible weight and length \(l\) is swinging in a horizontal circular path with constant angular velocity having time period \(T\). If the string length is shortened by \(\frac{l}{2}\), while the particle is in motion, the period is:

1 \(4 \mathrm{~T}\)
2 \(2 \mathrm{~T}\)
3 \(\mathrm{T}\)
4 \(\frac{T}{4}\)
Motion in Plane

144027 A child starts running from rest along a circular track of radius ' \(r\) ' with constant tangential acceleration ' \(a\) '. After time ' \(t\) ' he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]}{r g}\)
2 \(\frac{\left[a^{2} t^{2}+a^{2} r^{4}\right]}{r g}\)
3 \(\frac{\left[a^{4} t^{4}-a^{2} r^{2}\right]^{\frac{1}{2}}}{r g}\)
4 \(\frac{\left[a^{4} t^{4}+a^{2} r^{2}\right]^{\frac{1}{2}}}{g r}\)
Motion in Plane

144028 A body is moving along a circular track of radius \(100 \mathrm{~m}\) with velocity \(20 \mathrm{~m} / \mathrm{s}\). Its tangential acceleration is \(3 \mathrm{~m} / \mathrm{s}^{2}\), then its resultant acceleration will be

1 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(3 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144030 A bucket containing water is revolved in a vertical circle of radius ' \(r\) '. To prevent the water from falling down, the minimum frequency of revolution required is \([\mathrm{g}=\) acceleration due to gravity]

1 \(\frac{1}{2 \pi} \sqrt{\frac{\mathrm{r}}{\mathrm{g}}}\)
2 \(2 \pi \sqrt{\frac{g}{r}}\)
3 \(\frac{1}{2 \pi} \sqrt{\frac{g}{r}}\)
4 \(\frac{2 \pi g}{r}\)